He's awkwardly trying to make things a little better, stumbling his way, and he's used to only having to make small efforts in the past to accomplish the status quo of when you were physically intimate with him.
You've raised the bar much higher for that--does he know it?
I really don't think your husband has any idea how much you have raised the bar on what you want in a marriage, and I wonder if he will be the one to give up on it when he figures that out, perhaps giving up before you do, unless of course, he figures it will hurt him too much financially.
I'm wondering if he understands the level of effort you are looking for, and if he does, will he even be willing?
My ex once said to me--"I didnt drink for the last five days and nothing changed in YOUR behavior!"
Then he was right back to the bottle.
I believe he didn't understand that my trust could not be won back so quickly. I think your H thinks the same way...a little church, sleep in the bed, sober a few days, why isn't she responding?