'where they would all' vs 'where they all would'?

I see three variants as possible, and almost equivalent:

... trying to predict where they would end up.

... trying to predict where they would all end up.

... trying to predict where they all would end up.

The first of these is perhaps least problematic - it avoids the adverbial 'all' altogether. It also has the least implication that they'll all end up in the same place; it does not rule out different people in the 'they' going to different places.

The second of these might manage to have connotations that they will all end up in the same place (so a party of people might be going out to the same restaurant), and maybe the third manages to leave open the possibility that they would end up in different places (but you want to predict all of those places). However, that distinction is probably not really supported. I think they are essentially equivalent, which is why I classified 'all' as adverbial; adverbs are often able to move in a sentence with minor changes in meaning.

I don't think there are strong grammatical grounds for preferring the second over the third or vice versa, though I'd probably use 'they would all end up' myself. It could easily be a question of dialect, and a very subtle one at that.

You're correct; I can see no way that putting the 'all' before 'they' could be made to work without more major rephrasing:

... trying to predict where all of them would end up.