I think that self-answers should be ineligible for the Populist badge.
I agree with that part. The vote changing and editing part are just red herrings.
The main issue here is to get a populist badge you need to accept another answer, that the popular vote considers inferior to your own. This is probably deliberate, since you could simply accept your own answer if it's better.
It's possible that you post an answer of which you believe that it's inferior(But perhaps makes a point not covered by the other answer, so it's still worth posting), but the public disagrees and thinks it's better. That seems less likely than the alternative, so I think you shouldn't be able to get populist for answers to your own questions.