If we eradicate it in humans and also people stop eating bushmeat (or including chimpanzees or whatever in that category) then it seems to me like it would be unlikely to make the jump back to humans.

This actually raises an interesting question about potential diseases lurking in food sources. We now have 20/20 hindsight that eating an ape caused this and is therefore a bad idea. They obviously didn't know that when they chose to eat apes. There could be other such food sources that we don't know to be problematic yet. I am reminded of prions and mad cow, kind of a similar story.