Yep -- those are all the standard theories. However, what he will find is, even if he DOESN'T out her again, she'll STILL make him out to be the bad guy.
So it really comes to down to "a", what works, and "b", what HE feels he needs to do for his own personal integrity.
Personally, I don't think one can "push them together more" when they're ALREADY together, having an affair and cheating on their spouses.