Wouldn't it be nice if you just came to a fork in the road that clearly and definitively set the direction for the future of the relationship? As I know you know, it doesn't work that way. Just as it took H a long while and many mixed feelings to want to pull away from the marriage, the road back is likely to be the same.
I believe you have served your own purposes well by stepping back from his suspected affair and letting him wrestle with it on his own. Open and visible opposition to affairs too often simply gives them more emotional oxygen and justification for their existence.
Nor is it worth your time - for the sake of both your own sanity and your marriage - to snoop.
If there is an affair going on - which admittedly sounds quite possible - there is a high statistical probability it won't last long (read your copy of Divorce Remedy). My instincts tell me your approach has probably taken some of the thrill out of the affair - as your H must live in a state of uncertainty about what you know and a state of angst about whether he should tell you and a state of guilt over deceiving you. You're torturing this poor man! (I hope a little levity is OK) Meanwhile, the OW grows warts by the day as the initial sugar high of the affair wears off.
I believe you are still in a stage where you have to be extremely careful not to pursue - even in the tiniest of ways - photo posting on facebook of family pumpkin carving perhaps falls into this category. Let him initiate whatever happens for now. Listen. Soak it in and learn. Adjust.
Finally - I believe you are wise to understand that the marital issues that must be considered are bigger than just the affair - although that might feel like everything at the moment. I believe your understanding of these factors will put you in a good position to improve your relationship with H and set an excellent example for him as well - because at some point he will have to do his own work to make himself a worthy companion.
In the meantime, what a great job you've done with you. I know it's hard.