The whole Aiel/Tinker origin story has already been revealed. There's nothing really left for us to deal with. If there was more post-TG story, BS could have thrown something in about the Tinkers allying with the Ogier to help regenerate the supposed-to-be-fractured world (which wasn't at all, as you mentioned) using the Ogier-style singing that the AOL-Aiel were shown to be involved with. As it stands, the Tinkers are just a bunch of useless vagabonds who have an internal struggle that, to the rest of the world, is completely irrelevant, except for the few cases where their inaction results in harm/death to others.

The only large repercussion that TG had on the Aiel, in my opinion, is the fact that the Blight is vanishing, and so they'll have to now integrate themselves into the mainlands. What this means is completely open to speculation, since the issue just simply wasn't addressed. We didn't get a single Aiel POV concerning the future of the Aiel in AMOL. We saw buildup in TOM from Aviendha and her discussions with the Wise Ones concerning the future of the Aiel but...oops, I guess BS left that part out.