In your state, is there a law where one can prosecute/sue OW for loss of [can't think of the word right now, but it implies loss of income, affection from H, etc.]? If so, this is just the situation (and the OW), that one needs to do it, if it came down to actual divorce.
Also, if you sold the house, would your H get part of the profit? Surely, if he does, then he needs to pay toward the mortgage, air-conditioner, and so forth. In other words, the upkeep of the house. It would be in his interest to pay the mortgage, and whatever else that can be regarded as upkeep.
Otherwise, sounds like you are doing lots of GAL activities. Keep that up.
Take care.
Me:57 H:52 M:28 Got another lawyer last year and filed. D35,S/D twins28,D22 EA4/04 End? Who knows? "Life is like a mirror. Smile at it and it smiles back at you." — Peace Pilgrim