I don't think he does want to move out. At least you and H are in the same bed at night, my H sleeps on the couch (for months, his choice). Sounds like your H wants to be close to you in all this confusion.
My H is the same way, on the fence about moving out (even though I kicked him out for a bit when he confessed OW, he came back) and separating, stating it worries him that we will get even farther apart. Here's a clue, how about admitting the OW is definately making us farther apart? Oh no, let's just blame it on general problems, easier on H's conscience.
Awww the rings. H hasn't worn his in years and ironically my big diamond fell out the day before he confessed A. I joked to myself that while I was fixing my ring, maybe I could drop H off and have him repaired too. lol H took my ring in without me asking, and told me last week they called to say it was ready. I haven't gone to get it yet. Don't know exactly why.