You know H better than anyone, but it is not that unusual for people to cake-eat for months, even to continue living at home and have sex with both people off and on. People can fence-sit for a very long time. My friend's father had a 15 year affair while he was married and living at home.
If H's affair is not over (versus choosing OW), don't assume that means he will want a divorce, he may be content to "wait and see" for another couple months. He's clearly very conflicted. If H does decide to push for a divorce, there's nothing you can do about that anyway, that's outside of your control.
Forgetting about H and what he may or may not do, what do YOU want? If H does decide to sit on the fence for another 2-3 months, what will you do?
One thing I'm sure you've thought about is giving an ultimatum. The problem with ultimatums is that you have to be willing to enforce them. Usually by the time you're ready to enforce an ultimatum, there's no longer any reason to give one because you've moved on emotionally.
That said, if you decide that YOU cannot tolerate fence-sitting for another 2-3 months, then you can give H an ultimatum and tell him that he must go "no contact" with OW including changing jobs, give you full transparency, etc. by X date or you will file for divorce. Now if you lay that down and don't enforce it, you're in a world of trouble because you're no longer credible and he won't respect what you say.
Therefore, before you're at the point to do this, you have to have come to terms with filing for divorce yourself and facing your future without H. It's worth it to spend some time thinking about what you'll do if H does NOT decide and just continues to fence sit.
From my perspective, the best answer is to use the time to work on you, give H the space he wants, and set a longer horizon for your decision making -- i.e. "By the 4th of July, I will need this situation to be resolved, either H and I will be actively reconciling, or I will proceed with a divorce request." Then when you get to July 4th, you re-evaluate based upon how you're feeling then. Most importantly, you don't plan to make ANY decisions between now and then. You use the time to work on you.
Accuray
Married 18, Together 20, Now Divorced M: 48, W: 50, D: 18, S: 16, D: 12 Bomb Dropped (EA, D): 7/13/11 Start Reconcile: 8/15/11 Bomb Dropped (EA, D): 5/1/2014 (Divorced) In a New Relationship: 3/2015