I haven't read it in a while but I believe that "A Stitch in Time" by Andrew Robinson goes into a little detail about post-Cardassia. It also gives some good back ground on Garak.
If the UFP wanted to avoid another Kerensky/Weimar situation, they'd get aid in there and more importantly, de-Obsidian the Cardassian culture. Then again, there might be Cardassian interest in the Prophets. From a pragmatic Cardassian POV, the Bajorans' gods won the fight.