Five to ten years after TG, we know the Empress and Mat cross the sea to reconquer Seanchan...

It doesn't look at all like Tuon is in the middle of a war to bring down the Tower and secure an Empire in the Westlands, which means the conflict will somehow get resolved during TG. Egwene's dreams also seem to indicate this.

I also don't see any way in which post TG Rand would decide to force the world into a truce, or treat the Aiel the way he did in Aviendha's vision. He's much too wise now not to see this path leads to a world war after his death (or after he retires, as Rand clearly has no intent to remain in charge of much of anything after TG, and already is distancing himself from "rulership"

Whoever (or whatever... IMO, perhaps some kind of agent of the creator or a manifestation of the Wheel of some kind, perhaps a Hero of the Horn) she was, Nakomi tried to prepare Aviendha and make her think what the future of the Aiel would be, if they would or not return to their old ways after TG and if this was or not a good thing. In Rhuidean, Aviendha saw that the future was disastrous if the Aiel sought to remain warriors, return to the Waste and keep their old ways.

Aviendha's challenge is to find what the Aiel must become to avoid this future. LTT could easily guide Aviendha toward possible solutions.

I think it's terribly obvious Aviendha (and the Aiel) is wrong to think they were shaped to become strong just in order to atone for their "sin" by fighting and dying in Tarmon Gai'don. It's all there in TSR: the AS in Rhuidean have figured out they were wrong and the Aiel could not possibly remain the Da'shain Aiel until their purpose come, or they would all die long before TG, just like the Jenn did. They rather set things up so the Aiel would become what they needed to become to survive the Age, yet their leaders would never forget what the Aiel really were. The Pattern preserved the Way by scattering the Tinkers into remote, unthreatening small communities, and it preserved the bulk of the Aiel, made them strong in far more than war arts and hid them from the rest of the world for most of the Age Then, it forced the Aiel to come out of hiding, and made it so it was impossible for the leaders to hide the past from the folk as a whole, and also made it so the people would be reminded of how "savage" and "dangerous" the Aiel were by the scattering and the ravages of the Shaido, making them a target of the Seanchan Empire... So the Aiel must find a path where they would stop convincingly to be a threat, or that threat will be dealt with, by the Seanchan and some other nations resentful of their conquests with Rand. It's kind of terribly obvious the Aiel are meant to claim their heritage and re adopt the Way of the Leaf and thus become a threat to no one anymore. Aviendha just saw what would happen to them if they don't.

But as I said above, there's really no way LTT will ever let that future happen, all the more after Aviendha speaks of it to him. He knows how honourable and valuable the da'shain Aiel were. That's a big missing piece for Aviendha and company right now. They see no honour in their ancient ways. Rand will eventually set them straight about this. Their "sin", if you wish to call it such, is truly to have deprived the world of the da'shain Aiel for so long (but there was no other option, that's why "sin" is a misnomer IMO). It goes beyond simply abandonning the Way to survive. The way to atone for this toh and regain their ji is rather obvious but it will take someone who knows all about the da'shain, someone whom the da'shain revered and served in the WOS, to set the Aiel straight about there being no honour and purpose in this way of life, someone who can tell them the Aiel used to stand just a small step below the AS in the respect of the AOL people., and respect in the AOL came from the value of your service...

A part of it, and perhaps a small part of it at that (the Guide implied as much), is that in the short term the Aiel are the ones who can continue Rand's efforts to feed the world after the ravages of the LB. They do have the power to sing to crops, and post TG - in the summer where virtually no farmer will grow anything, this will be invaluable (otherwise it's the fauna that is in danger of getting decimated to feed the people next winter...).

I think a new Covenant between the Aiel and AS will emerge before the end. That will play a major part in averting the future Aviendha has seen. The other aspect is the resolution of the conflict between channellers and the Seanchan. There, the solution seems obvious as well. Egwene has the people with her now who can destroy the whole Seanchan system. Egwene can produce sul'dam who can channel and prove that all of them can learn. Whatever Tuon thinks, she'd be finished if this truth comes out, at least in uncontrolled conditions, with her unable to spin it - the new Empress is marath'damane, knew it and hid it. Worst, there's no proof that Tuon didn't already know, that the Paendrags have always known. This will shock many Seanchan minds to the core. By hiding the truth about sul'dam, Fortuona has lost the moral high ground, and reduce the Return to a war by a group of channellers at the top of the Empire to eliminate a rival, and for millenia non-aggressive, group of channellers. What's less obvious is how the WT can help Fortuona to preserve and reform her Empire. I think the three Oaths and the Binder might come into play. The Seanchan sul'dam could swear binding Oaths to the Throne that would make them as "safe" as the a'dam, without the slavery. I think a deal the Seanchan and WT might strike is the freedom of all damane and sul'dam, who could choose to swear Oaths of allegiance to the Empire (which will most likely continue to allow the use of OP in battle), or to remain in the Westlands and join the Tower. All this would require, technically, is Elayne making a copy of the Oath Rod for the Empress.

The ultimate fate of the Seanchan "provinces" is more uncertain, but a solution could be for Fortuona to federate them under the other legitimate Paendrag heir,: Berelain, then prepare to move her Imperial armies back to Seanchan to pacify it before it leads to an intercontinental war. Tuon has done some great things in the South, it's not all bad. Altara especially is much better now than before the Return, and so is Amadicia and evenTarabon. This work could be preserved under someone more acceptable and not antagonistic to the Westlands culture, like Berelain. With Galad as her consort (and a possible ruler for Amadicia), this "federation" would be tied closely to Elayne, Galad's sister, and Elayne doesn't know it yet, but she's already tied by blood to the soon to be Queen-consort of Tear, another Damodred, who has already spoken of agreeing to Elayne's rule of Cairhien... So it's look more and more like the post TG world could turn around a House Trakand/House Damodred global alliance. Heck... even the likely husband of the Amyrlin Seat is a Trakand by name and half Damodred by blood! Elayne is emerging more and more as a merge between a less imperialistic Hawkwing and Mabriam en Sheered.