FT, count me as another who just sucked it up and moved out after my STBXAH SAID he would move out, then the very next day acted as though nothing had happened. Unbeknownst to me, we were two months behind on rent. I had to borrow A LOT of money to catch up on that rent so my landlord would give me a halfway decent landlord reference. Even then, I still had to prepay my last month's rent to get my current landlord to rent to me (more money borrowed). AND I had to pay down a big balance with the utility company before they would move my service to a new address (still more money borrowed).
Fact: by your own account, your AH's behavior shows basically NO real commitment to sobriety.
Fact: even if he WAS committed to sobriety, you still need time and space, and his sobriety journey would benefit from the same time and space. A separation would still be a good idea for everybody even if he was devoted to his program.
When I moved out, my three children and I ended up in a small, 2-bedroom apartment. I sleep in the living room. And we are all happier and more at peace, than we have been in over 5 years.
I understand the practical considerations you are facing. I had a lot of them, too. I ALSO used them as excuses to postpone leaving. If it were me, I would call the current landlord. Figure out how much time is left on the lease. Figure out the penalty for breaking the lease. I agree with whoever upthread said that your AH's ability or inability to pay rent is his problem, and you shouldn't continue to live in misery because of it. You can notify your landlord that YOU will be moving out and breaking the lease, and your AH can do whatever he wants to do, rather than having you (purposely and inadvertently) shielding him from the consequences of his behavior.