To be honest he is a living paradox. You ask him why the world has to be sacrificed and he says he doesn't want to tell you too much. Then if you say you'll prove him wrong, he says he would treasure that. Quite how you are meant to stop him by persuasion when he refuses to give you any hint as to why it is so essential to go through with his plan, is mind boggling. Why couldn't at least give you a clue to go on if he wants you to stop him? I think it is more of his patronising praise that he has used before without apparently being sincere. Even if he thought you were incapable of stopping him, surely if he secretly hopes you will, he would point you in the right direction?
The declaration made by the Inquisitor at the end makes even less sense: how are we going to save Solas from himself when we have absolutely no idea what the pre-requisites are?
For example, I have a theory that the reason he feels he has to reset the world is because of the Blight and red lyrium. His original action was to stop it from rising up from the Deep Roads and now that it has, he feels its destruction of the world is inevitable. So to get him to change his plan, you would have to show that it was possible to cure the Blight/remove red lyrium. All he had to do was admit this was the reason for his action. You have still then to come up with a way of proving you can stop its progress before he will abort his plan. As it stands, you could spent futile effort on this because even if you could succeed in coming up with a way of curing the Taint, it might turn out this had nothing to do with why he had to do it.
Alternatively, he could be under a geas from Mythal to go through with it. So the way to stop him and save him would be to break the geas. But to get anywhere you need to know. If it was a case that he was not permitted to tell you, he could at least hint that was the case; not suggest that he didn't want to tell you too much.
I personally think it would be much easier to persuade him to stop than to kill him; since to do the latter you have to get near enough to him and that is nigh on impossible since he can petrify you with a thought as is a powerful dreamer, unless you can find an equally powerful dreamer to attack his mind in the Fade.
If he wants you to stop him sub-consciously, that is no help at all since he isn't even aware of it himself.