Sounding cautiously positive! The fact that he's the one looking into signing you up for the weekend program is a good thing-- I might recommend not pushing and not mentioning it, letting him get you both signed up all by himself.
What is his deal exactly with his other place and work situation? When does his lease there end (do you know)?
When you say you were intimate once but tried a few other times-- was that you initiating and him saying no? (or just too much booze?)
It sounds like he's definitely making an effort, and probably nice for you guys to spend time with friends together and have it be relaxing and fun, and he can see that it won't be all strange because of the situation. I think it is also a good sign that he was excited to introduce you to new friends of his etc. I agree not to push on the move or anything-- in fact one nice thing about him being gone during the week is it really gives you a little space to reflect on what is and isn't working. Last week it sounded like you asked a lot of permission before physical contact-- is that still happening?
Fingers and toes crossed for you, SamCal... sounds like things are definitely improving! Keep up the DBing and I would also caution keep your expectations in check-- seems like the road is never straight and you don't want to let a curve throw you off your game.
Me (46) H (42) M:14 T:18, D9 & D11 4/19 - 12/19: series of escalating BDs 9/20 - present: R and piecing