I'm fairly convinced that Solas's goal (be it destroying the veil or freeing the elven gods) will be accomplished in either DLC or an expansion before DA4, and DA4 will have a new protagonist having to deal with the results.
1) If either of those things happen, Tevinter seems like the place to be for the most exciting stuff - they're the group most likely to be at odds with any elves who come to power, and where the most mages will just go crazy if the veil was gone. And rumor is the next game will move to northern Thedas.
2) It would make sense for the Inquisitor to not be involved in the saving the world bit, if Solas needs the anchor in order to succeed in his goals. Which would make the Inquisitor either his willing accomplice, unwilling servant (power of mythal), or dead.
It just doesn't seem like an interesting game, to me, for DA4 to revolve around random new person finding out about Solas, and chasing him around Thedas trying to foil his plans. That's basically what we just did in DA:I, the difference being that if that were DA4's plot, half the players would not want to fight their "villain."
Everything you said is what I think.
If the elves gain immortality, think of what will happen in Tevinter! It'll be madness.. It's the next gen of mage-templar conflict.
Plus, I also imagine that Quizzy will be used to achieve what Solas wants to achieve, because of the anchor. If Quizzy complies it will end peacefully, Quizzy lives, but will probably have to disappear, since people will hunt Quizzy down (a good excuse to make Quizzy disappear, better than the excuses given to HoF), on the other hand - if Quzzy refuses Solas kills Quizzy and uses the anchor.
We need a setting for the next game, having a new protagonist chasing Solas around without even knowing who Solas is in the first place (Solas won't be a known figure before he accomplishes his goal), kind of weird? I guess they can make up a entirely new story but it'll have to be at least as epic as dealing with the consequences of Solas' actions. I'm pretty sure that since people got a vague idea of what Solas wants to do they'll get annoyed if the next game will deal with anything that isn't as big (I know I will, I'd be like "that's all nice and dandy, but I want the world to flip already!").
-Waves team optimism flag yet again-