I lean more to the former idea. Rand is a different person in the sense that he has had experiences and influences that Lews Therin did not and was raised in a different environment. He even has different biological imperatives, since his genetic make-up is different. But he WAS Lews Therin, he had Lews Therin's body and whatnot, and forgot it all when he died and was reborn, but due to his special circumstances, he was able to access that stuff to a degree. Channeling is not really CAUSING the two-way memories, so much as it is a thing that both have in common, so dealing with the channeling, especially with no training or techniques to impose any expectations or perceptions on his experience, is a common link. When grasping instinctively at saidin, he is reminded on a metaphysical level of his prior experiences doing the same thing. If saidin enhances the physical with the heightened senses and extended lifespan, or allows Rand to tap into his genetic memory (the dai'shain of the AoL would certainly not have had the Aiel mantra of screaming defiance with the last breath and spitting in the Dark One's eye, so Lews Therin would not have known it), it stands to reason that it can enhance his awareness of himself at the metaphysical level and reach back to some deep-down understanding of the One Power.

I tend to doubt the taint as a primary cause, though it might have played a part in distorting his memories or bringing the most painful to the forefront. I think a very good explanation of the extreme to which Rand takes his issues with killing women is that in his subconscious he is recoiling from the memory of Lews Therin killing Ilyena and his guilt over it. Ishamael states that Shai'tan's Healing, presumably meaning with the True Power, is not like normal Healing, so I think Lews Therin was not restored to sanity but rather had an altered clarity imposed on him, with a malicious filter that emphasized the worst of his memories and actions. One of the understandings of Satan, on whom the Dark One is at least partially based, is the Accuser, someone who sees the worst in people and resents them for their sins and crimes, and rebelled against God over Divine mercy and redemption. The taint seems to work this way as well, and it fits with other descriptions of evil forces in general, from the paranoia and imposed by Shadar Logoth influence, to the altered behavior of the populace in cities controlled by Forsaken. The slovenly standards of hygiene displayed by the Whitecloaks in Fain's retinue and Tar Valon under Mesaana, as well as the malaise in Tear under Belal, suggest a lack of self-respect and pride and the hair-trigger violence in Illian and scheming in Caemlyn seem akin to the paranoia and hostility Mat displays when carrying the dagger. And Rand, especially the LTT persona exhibits many similar tendencies. He tends to be rather indifferent to his own well-being and condemns himself harshly for minor transgressions or thing that are not really wrong or his fault, and he is quick to anger and lash out and experiences at times inordinate suspicion.

So I think the taint's influence on the connection between LTT and Rand is not facilitating it, but distorting it and bringing out the worst in both, and amplifying Rand's own trauma and Lews Therin's guilt.

The reason beyond what we see of Rand and LTT why I think they are the same person (as opposed to a soul coopted into a construct like a Trolloc or a Nym and then [hopefully] reborn as a human - that human is not a Trolloc or shadowspawn reborn), there has to be some continuity in retaining the role from life to life, and something why THIS reincarnation is special and metatextually, why no one else is legitimately identified as another reincarnation. I don't believe one (or all three in a split soul thing) of Rand's love interests is the reincarnation of Ilyena or that Egwene (or anyone else) is LPD reborn. Mat's memory of leading Manetherin troops in the Trolloc Wars in tDR during and after his Healing is not a reincarnation memory, but a genetic one. He's not recalling a past life, but an ancestor, more like Rand was in the glass columns of Rhuidean, or picking up the Aiel mantra when encountering the Choedan Kal.

But back to my point, why does it matter than some rando soul who just happened to be Lews Therin in a past life, but has none of Lews Therin's position or connections or expertise that made him a leader in his world nor his personality or characteristics imbued by nature and nurture that allowed him to save the world last time, be responsible for confronting the Dark One and leading the forces of the Light once more? Rand/LTT is a special case, a designated champion or representative of humanity and the Light, a defender of the Pattern. Because his role is the same, he has some continuity from life to life, because it's relevant. Other people, not so much.

Whether Mat's soul in the War of the Shadow was a powerful Aes Sedai, a military leader or a random grunt, it does not have much to with his life now, as a wild card responsible for messing up the plans and gambits of the forces of disorder and as a commander of entirely different kinds of people and weapons in the latest climactic confrontation with the Dark One.

Even if Egwene WAS LPD reborn, what she did as a political leader of the post-Strike Aes Sedai and military leader of the mop-up efforts against the Shadow's forces has no relevance to leading the modern White Tower. For all that military officers and pretentious civilians like to read and quote "The Art of War" or "De re militari" or "On War", SunTzu or Vegetius or Clausewitz would struggle to command troops in each other's time and place or modern times and contemporary military experts might still be hard-pressed if finding themselves in command of pikemen, archers and horse cavalry. The correlation of personalities and rules and societal practices one must understand to be effective politically is very different in the end times of the two Ages. Because the Wheel turns.

But Rand's battle and his mission were never military or political or about channeling. Lews Therin's failure, such as it was, and the extent to which Sanderson accurately has him say he failed in the War of the Shadow, as well as the extent to which we can make informed suppositions about the nature thereof, was that rather than confront the Dark One as Rand did, he attempted a military/preternatural solution to a metaphysical problem (I think the One Power is really a physical element, as opposed to metaphysical, given that it's an energy source that behaves on natural principles, rather than an appeal to some greater or higher force as in rituals). He tried to gimmick a solution to the Dark One's power, rather than truly defeating him on a moral level as Rand does. Rand's attempts to be a worldly leader tend to fail, even his penultimate action of imposing the Dragon's Peace, as we can infer from Aviendha's future visions. He does much better inspiring people to change and to take up roles in the cause of uniting humanity. As a politician or general, he becomes, by the nature of those functions, divisive. Politicians take from one party to give to another. Generals fight others. Kings are both. Lews Therin was both, and Rand outdoes him and wins a true victory by transcending those roles and rising above the mundane struggle to morally defeat Shai'tan and reject him on behalf of the world. Ultimately, the responsibility for organizing the world and day to day stuff has to be done by the people involved in it, rather than an ideal situation imposed by a super-leader.

In this, I think WoT is heavily borrowing from an aspect of the Christ narrative, whereby the Pharisees and many other Jewish people expected the Messiah to be a worldly and political leader who would restore the sovereignty of the Jewish state and lead it to worldly prominence and dominion, and are disappointed, because the point of that story is that Jesus came to morally save people and show them a way to be better and attain spiritual salvation. Now WoT is clearly not the same story as no one is positing Rand as a spiritual savior or a representative or aspect or avatar of the Creator, but there are similarities, in that his mission is to save people from an oppressive force that will not just kill or compel them to slavery, but prevent them from being their best selves. In the alt world ruled by the Dark One, people are encouraged and compelled to be evil to one another, with betrayal and cruelty encouraged and made into a way of life. There is no way to be good in such a world except by quickly becoming a victim and at best a martyr. By ridding the world of the threat of the Dark One, but not imposing his own rule, Rand allows people to CHOOSE to be their best selves, rather than force them to act in a good manner when they have no other choice. When things are falling apart and people choose to stand up for what's right, or reject the incentives to selfishness, it's more heroic than if doing the right thing is the only option available to them. In large part, that was the flaw in the AoL, where they really DID manage a utopia, but made it too easy for people to just be good by default, and when the Dark One presented other options, way too many of them failed the test. Lews Therin's greatness is not his stature in the AoL that got him an honor name or garnered him status and respect, it's how he behaved when the chips were down and all seemed lost. And however flawed his perception of what was needed of him, he DID save the world and buy humanity a three thousand year respite from the threat of the Dark One, more than enough time to be better prepared to resist the Shadow once again.

That too, is why I think Rand was deliberately placed in a situation where he was would be raised in obscurity, and why the Pattern hid him from Moiraine until the last minute, because it already tried putting its champion in a starting position of great power and influence, except he was bogged down by temporal concerns and perspectives. Just as Rand survives Daes Daemar by refusing to play, and outstrips Moiraine's goals in Tear by refusing to go to war or play politics and wins over the Aiel despite refusing to pander to them or play along with the 3,000 year old cultural lie, he ultimately frees himself of the trap Lews Therin fell into by delegating the temporal battles to political and military deputies. Demandred was ready for Rand if Rand came at him with armies, the Power or a sword, but Rand said "Nah, Imma concentrate on your boss" and let Mat, Logain and Lan handle him on those levels. Demandred tried to match and better Rand in every way he thought possible, and probably succeeded, but Rand transcended him. It was the ultimate pissing contest and Rand won it by not playing, and thus not getting any piss on himself. Note that despite making himself out to be the ultimate leader and hero-type, Demandred is NOT Nae'blis. That job goes to the only one of the Forsaken really operating on the moral level, who sees what it's all about, and the long-term stakes of the struggle in terms of Ages and the Wheel, rather than the Pattern of the current Age. And it's on that level that Rand engages and defeats him. It's Rand understanding the victories of the people, the other lights fighting the shadow in Min's graphic representation, are not losing, but winning through their choices, not their temporal state of affairs. "...still fought" not "gained the crown/took the field/won the duel".

With that as the stakes, the Dragon needs the perspective of both lives, he has to see more than just what this person or that knows and has experienced. The particulars of the setting of the Second or Third Age does not matter nearly as much as choosing to reject the Shadow and all its works and all its pomps. The Dragon is allowed continuity between lives because his role is more important than either of those particular threads in the Pattern called Lews Therin and Rand al'Thor.

So, no. I don't think it's the taint eating away at the barriers. Or rather it might be one of the symptoms, since the taint rots the physical body as well, and could very well erode the merciful separation of lives that protects other people and allows them to live and make choices unhindered by the perceptions of now-irrelevant past lives, but I don't think it's happening with Rand, anymore than his physical body is showing signs of affliction from the taint.

In the end, the soul of the Dragon remembered his experiences and feelings and knowledge from his life as Lews Therin, but he was not actually Lews Therin. That man died when he overchanneled and created Dragonmount. Rand al'Thor is a new person, a blank slate who was formed and shaped by his upbringing in the Two Rivers, and later downloaded the memories and experiences of Lews Therin, but which no more changed who he was than he became Rhodric or Jeordam or Coulin or Charn or Jonai or Adan or any of the Aielman whose lives he experienced in Rhuidean. Lews Therin's ghost was also not talking to Rand, Rand was in denial about his thoughts, because as Robert Jordan responded when asked by WoT characters fear death knowing they will be reborn, he wants to be himself, and not another person with different ideas and values and formative experiences. It's a parallel struggle going on in all the ta'veren, with Perrin and Mat also resisting the wolves and Eelfinn memories, because they want to be themselves, not an animal or an amalgamation of long-dead military officers and adventurers, respectively. What all of them have to learn is that things like that do not define them, that they and they alone are responsible for their own choices, and those choices are what make us who we are.

That's the ultimate struggle for everyone in the Wheel of Time, to make choices for the good and right and be true to the best version of themselves, without letting other factors imposed on them dictate who they are. They have to accept their experiences and circumstances and teachings, without letting those things dictate their identity. Egwene has to learn to be her own kind of Amyrlin, not an actor in Siuan Sanche's revenge drama. Perrin has to be a man, not a child who is told what to do or a whipped husband or an animal, and that includes taking responsibility for things he does, like kill Children of the Light because he's pissed, not because a wolf "made" him do it, while also allowing that other people make their choices, such as the men who died following him in the Two Rivers or at Dumai's Wells or at Malden. Mat has to learn to take action to protect others in ways he sees as oppressive, because of his inclinations to self-indulgence. Lan has to learn not to let the dead or the customs of Malkier define him and choose his life path, but in the end, he too, must accept that other people have the right to make their own choices and choose to fight and die with him, instead of assuming it is because of him. Moiraine has to learn that she is a soldier, not the general; a musician, not the conductor; that she does NOT know what is best for others. They all have to learn, to, both at the same time, step up and let go, in varying degrees for all the protagonist characters. Other characters who are not the heroes of the story, both good and bad, like Pedron Niall or Elaida or Siuan or Gawyn or Aram or Moridin or Demandred, fail at one or both of those things, even when, like Niall and Ishamael, they grasp the nature of that conflict to a degree. Some, like Ingtar, learn it too late to be heroes, but in time to save themselves.

What this all means to the issue at hand, is that by understanding what the story is about, what the important conflicts in the narrative are, we can get a glimpse of the intent of the author in depicting certain aspects of the setting, so even if the in-narrative explanation does not satisfy, we can infer what the point of the incident happens to be. It fits better if Rand and LTT are not separate people. If they are, LTT is just another external opponent, like the villains or Moiraine or Alanna or the villains or political opponents or military adversaries Rand has to face. His internal conflict, the war his heart is fighting with itself, to reference Faulkner's aphorism about the only stories worth telling, is against the old part of him that went mad, that was physically defeated by the Shadow and that was so caught up in the world and temporal matters he did not see in time the real fight against the Shadow. It's also a war Rand thinks he is fighting for his own identity as Rand, son of Tam, of the Two Rivers. He wants to stay an al'Thor, not become a Therin, to be the love of Elayne and Min and Aviendha, not Ilyena, like Perrin thinks he is fighting against Young Bull or Mat against a bunch of dudes who lived a millennium or two ago. If Lews Therin is someone else, than Mat & Perrin are also in real danger of possession by the memories or a wolf nature.

Basically, it HAS to be the same guy in both lives, for the story to work as it does.