I'm not sure it would be actually working, since users don't read, but could be worth trying.
A case which happen quite often is that people will add new details to their question as a new answer, like they would on a discussion board.
The current warning which appears when you try to answer your own question is the following:
Are you sure you want to answer your own question?
If you're responding to answers left on your question, use the comments link under each answer.
Would it be worth to add one more sentence to it, stating something like:
If you are adding details to your question, do so by editing it.
The risk is that it will add one more line, reducing then the chances for someone to actually read it before just clicking ok. But it could help with people who don't know that they shouldn't do that. Not all of them, of course, it won't prevent people from just dismissing warnings and do what they want. But it could be worth adding this information, for the ones who want to follow the rules, but who haven't read/understood the FAQ yet.