No lock changes is the right way to go. You're (unfortunately) at the beginning of a potentially long journey that may be fraught with moves and countermoves. At this point you don't want to be seen as obstreperous. That can come back to bite you real hard!
Just enjoy (and encourage) his absences whether for work or gigs. You no longer have to worry about what he's doing, you already know. Shitty knowledge, but better than uncertainty.
If I were you, I'd keep asking him to leave. Ask him every single day, especially if he starts in as 'fun H' or 'irresistibly seductive H' (bleah!). Not in a nasty or angry way, just 'So, how are your plans for moving out going?' as if it's a foregone conclusion in your mind that he will be leaving, sooner or later. If he argues, simply say 'You already know how I feel and I'm not changing my mind' or words to that effect.
Keep doing your background financial work and document gathering. Also, if there are pictures or other small things, things that won't really be noticed missing, that are special to you that you worry about him either taking or destroying, you may want to consider moving them elsewhere. I think I can pretty much guarantee that at some point, when he realizes that you are dead serious, he is going to get angry, very angry and want to hurt you. Not necessarily physically, but to cause you to feel the loss (if that's the right word) that he will be feeling. My ex took some albums that I'd had since I was a teen. The music on those albums were the 'story of my teen years' and you couldn't find replacements (this was decades ago, thank God now for digital music!). He could have cared less about the artists, he just wanted me to hurt.