I ask since the main reason H is continuing to want his AP is because he says that he finds me attractive but does not desire me, and therefore does not want a life without that.
What a pile of steaming horseshit this is.
Stop listening to his words and start watching his actions. He doesn't find you whatever, because he is still involved w/ OW.
YOU Cannot FORCE him to stop, YOU Cannot NICE him back. But what you can do is stop tolerating his abuse. When he says shit like this stop him. Say no. I will not listen, it is not true, you are lying to me and if you believe it you are lying to yourself. Until you can be honest and have your actions match I want nothing to do w/ you.
Then you move his ass out of your bedroom if he is still in it, put him in the basement, the hall closet, or the backyard. YOU are being abused and tolerating in hopes that he will see clearly soon. He won't until he knows you won't be there waiting for him to change.
Read up on the 180. This was meant for you very situation. Hopefully this will wake you up from your fog. Give yourself a timeframe for change, and if you don't see it in him by that date you file. I know D isn't what you want. YOu cannot have a healthy M w/ this person. He has to stop, and be transparent, and start doing the real work of R for you to even consider not D'ing as far as I can see. Anything else is only going to cause you significant pain and harm.