For the verbs that go in the middle of compound verbs, is that always the case? I can't say "j'ai mangé beaucoup "?
'Vite' sounds strange to me in that position--"j'ai vite couru". Even Google Translate used "couru vite", although it's certainly not the final arbiter of good French :P
I'm also having a hard time finding an example with bientôt. Maybe "je vais bientôt arriver"? That's another one I would intuitively reverse--"je vais arriver bientôt ".