With the full memories of LTT, after the fashion he is a master of time travel.

Before and during TG Rand won't have time to bring back anything but the essentials, and no doubt his vision of the AOL is tempered with his experience of his life as Rand (in the sense that even with the memories of LTT, Rand isn't a die-hard admirer of everything and anything AOL. We could see this even in the way he dealt with Egwene, where it really transpired that LTT/Rand aren't without reservations about Aes Sedai, then and now). In other words, there are many things about the AOL Rand probably don't wish back.

But it might happen that Rand survives TG, or it might happen that LTT judges that world needs the talents of the Da'shain. We know he had a special relationship with them, and it's surely no coincidence Jordan has chosen not to reveal any of the specifics at this point. We don't know if the powers are strictly hereditary, if they can awaken without following the philosophy and many other questions of this kind. It may well be the Tuatha'an's blood is too diluted by now for them to have retained but a scrap of the Da'shain's talent, but this wouldn't be true of Aiel. It's not impossible however the Tuatha'an's Way of the Leaf is by and large still "pure", having barely changed since the days of the Da'shain (Rand would know for certain). Some Aiel prophecy say the Aiel mustn't fail the AS again or they will be slayed. So WO believes it could mean the Aiel will at some point serve the AS again. Some readers believe this was their prime motivation for "teaching" Aes Sedai, because they can't even consider serving women like the AS are now. They happen to shape one according to their moral standards, and she happens to be the Amyrlin Seat now, and to seek to tie the WO to the AS again. Egwene doesn't have any prophecy in mind doing this, but I doubt it hasn't occured to the WO yet that Egwene may have put in motion the chain of events that will lead to the Aiel serving the AS once more. She intends the WO to transmit their ethics, that may be closer to an aspect of AOL da'shain service than we know, at least it sounds to me quite credible that being their servants was traditional, perhaps even symbolic but most likely the Aiel had a far more important reason/purpose to live near Aes Sedai than housekeeping. There's likely some sort of symbiotic relationship we still know little about.

So basically, the key could be to reunite the Tuatha'an with the Aiel. The Tuatha'an would merge with the WO as the "spiritual class" - the Tuatha'an more like theologians, the WO more like priests (some of the titles of the Tinkers's leader are but a variation on Wise Ones...it's really possible their common origin is in the forgotten spiritual leaders of the Da'shain), but the talenst would only arise among the pure blood Aiel (that would be like RJ, I think... 2500 years of looking for "A Song" which is actually a Singing talent, only to find out when they finally learn the truth that the Tuatha'an themselves can't do anything with Singing because they've left the Aiel and their bloodlines havehas lost the talent), while the Aiel can't use it because they have abandonned the Way. The Wise Ones, incidentally, have a strong tradition of teaching... and one of their fields is an elaborate moral code they transmit to the warriors, part of which is a distortion of the Way of the Leaf. Making the Aiel return to their older code would be difficult because it changes so much their beliefs (the most radical difference is between being a da'shain versus being a gai'shain. Being da'shain isn't a way to regain your honor.) , but in many ways the Aiel have the best cultural outlook to be able to slip into the Way of the Leaf fast (quite a few of the beliefs and traditions are the same, for instance the Aiel's view of death is extremely close to the Tuatha'an's), especially that their "original sin" and atoning for it are notions solidly ingrained in their culture, it's just that they atone for the wrong sin and the wrong way. In the right time, and with the WO presenting this the right way (they're the first ones who need to be convinced...), Aiel could very well see it as a matter of ji'e'toh to re learn the Way, especially if Aviendha is convinced that not doing so and remaining warriors lead straight to their doom.

In any case, the prophecy can (typically) be interpreted in so many ways... It does appear to be about the Aiel who are warriors and it tells them they aren't real Aiel, merely call themselves that ("those who call themselves Aiel", as opposed to those who were the "True Aiel", the Jenn. But if this includes the Tuatha'an or not can depend massively on when this prophecy appeared. If it was made early enough, the Tuatha'an too called themselves Aiel, and they too were "so called" because they were dedicated to the Way, but had abandonned their dedication to the AS (unlike those who became the Jenn). We'd really need to know what "da'" - which really seems like a contraction of a longer word - stands for - the key to fully understand what the Aiel considered themselves dedicated to is in that word...

The prophecy also tell us the Aiel's bonds to Rand can't be broken, and that he will destroy them.

The "remnant" could easily refer to the small percentage of the Aiel warriors Rand will manage to convince to return to their old ways, and it doesn't rule out the Tuatha'an having a role in this (even if they're not included in "those who call themselves Aiel". Such an interpretation is reinforced by the previous verse that says Rand will break the "so called" Aiel with the Leaf and break them like dry twigs. Nothing says that verse has been fulfilled already... especially since it starts by saying he will spill their blood like water on sand, then he shall break them with the Leaf etc. When Rand "broke" the Aiel with the Leaf - or rather what we think was the fullfilment of that verse at al'Cair Dal, he had spilled none of their blood. Jordan's prophecies are usually realized chronologically, the order of the verses is respected. The prophecy doesn't say Rand will break the Aiel with the Leaf then spill their blood - it's worded in the opposite order - and it can be argued what he did at al'Cair Dal hardly constitute "breaking them like dry twigs". The "breaking with the Leaf" may not have been fulfilled in TSR just because the characters think so (wishful thinking that this "breaking" didn't shake the Aiel to the core after all? Only a remnant of a remnant even qualifies as "broken"! Most Aiel were a best disturbed, before they took it in stride and forgot what happened to follow the CoC), but refer to something far more radical/fundamental soon to happen to the Aiel, after Rand has spilled plenty of Aiel blood since leaving the Waste. Rand had but a vague and incomplete idea of what the da'shain were in TSR, and it's the same for clan chiefs and WO. They were pacifists, and they served Aes Sedai, and they had special powers... and the AS in Rhuidean seemed adamant that it was vital for the Aiel to survive to play a role, and were initially convinced it was their beliefs and pacifism that were vital, until they finally understood the Aiel couldn't survive unless they became Warriors, but the Glass Columns is evidence enough they never stopped to believe that it was the beliefs/da'shain ways that were important, that one day the Aiel leaders would have to bring them to that. It doesn't seem to have occured to many readers yet that the second vision Aviendha has seen may have been triggered because the ter'angreal was keyed to her all along, that her passage through it was an event foreseen, that the vision may have been the murky future (a variant, only Aviendha would see the events precisely through the eyes of her descendants, but any Aiel who triggers this other function of the ter'angreal may see similar events through his own descendants, just like by passing through they see key events of the past, some of them always the same, but from the perspective of their own bloodline) the Rhuidean Aes Sedai all along saw and which convinced them the Aiel must not become warriors and break "the peace of the Dragon". These Aes Sedai would have known these were events from the time of the LB, that victory would lead to a horrific war and horrific society if the Aiel continued this war. This could well explain why the AS took so long to understand the Aiel had first to become warriors to survive, and only at a specific time return to their past. I think Aviendha triggered the vision because her children are of the Dragon Reborn's blood, or because of her bond to Rand. This "reprogrammed" the ter'angreal to show this woman the future of the Aiel she is meant/prophecized to avert. The Glass Columns may have played the final role its makers always intended. I wouldn't be surprised we learn later that with its purpose done, it has now shut down and doesn't work anymore. It is something that may well happen, because some of the WO likely won't believe Aviendha and send WO to Rhuidean to try to see that doomsday vision. Learning that the ter'angreal no longer works but doesn't appear broken might convince a few this means its purpose is fulfilled, that there won't be any more WO and chiefs chosen this way - a sign from the AS who made the thing that their days as warriors are over - and Aviendha's vision explains why. I can't see even the WO as a whole accepting this or this interpretation, perhaps only a core group around Aviendha may remain, and this group and the warriors/chiefs who accept to follow them may be the seed of the final remnant of a remnant. There's a good possibility the WO suspect something about Aviendha they have not told her - I think they may have been Dreams or Prophecies guiding them toward a match with Rand. Some WO seemed quite intent that the time for Aviendha to become a WO and marry Rand has come. In any case, who else than Rand the WO (Aviendha) can turn to for more knowledge of their past so they can properly guide the Aiel to their final purpose so he can save that remmant of a remnant they now believe are those who accept to follow this path back to the Way? This could be when Rand actually "breaks the Aiel with the Leaf" - when he does explain what the da'shain truly were, why they chose to serve the Aes Sedai, what were their talents and values. This could be the WO who choose then to seek the Tuatha'an... who are with the Seanchan.

Another possibilty is that the Ogier Garderners, on the continent that wasn't as much affected by the Breaking, and who still serve society (they merely switched their alliance from the now corrupted AS to those who kept society in order and peace...) remember the Da'shain Aiel and Singing when the Tuatha'an do what Tuatha'an always end up doing and ask the first Garderner they see about "The Song". Not enough to teach anything, but enough to make the Tuatha'an realize they once were called the Da'shain Aiel.

(An interesting plot twist, an unlikely one, is that Tuon's Gardeners, between the Aiel prisoners and the Tuatha'an, figure out these must be two branches of the original da'shain Aiel, and that those da'shain Aiel once had useful talents for the ruler of a now starving world... and told Tuon. A few Seekers' jaws would drop to the floor if Tuon asked them if they can still Sing and what they remember of the Da'shain Aiel!)

The bottom line is that it's all way too clean... Rand/Aviendha have the Aiel, Tuon has the Tuatha'an. We have two groups of Ogier with no doubt complementary portions of knowledge due to their different histories, who we know will meet. With Merrilor, Rand fulfills one part of the Finns' riddle, bringing east and north together as One (notice the riddle don't say Rand had to bring it about, just that the world needed to get to this point). Tuon (not Rand) has brought the West and South together (ironically Rand has tried to make the wrong combo true, by uniting South and West together with his Arad Doman blind wild guess which was always more about following that riddle than accomplishing something really logical) A key to the LB according to the riddle is to bring these two groups/alliances - the one that will soon form at Merrilor and Tuon's - together "as One". When this happens, the pieces will at last be in the right place for the resolution of the whole Aiel/Tuatha'an scattered/separate story threads to merge as the final resolution for both groups. Likely for the Ogier as well, not to mention yet another important key point in Egwene's storyline. This will also reunite Mat/Tuon etc. The two groups becoming one sounds like a very important cornerstone (which makes me think it won't happen too early in AMOL... an event likely to occur some way into the LB only).