Do you sleep on a twin OP? Would there really be no room for you to just have her sleep at your place, maybe a few sets of clothes, and keep the rest of her stuff in storage (renting storage for a few months isn't that expensive at all). Maybe one year in is soon for you to be moving in with a significant other and that's compounded by this so I'd understand that, but unless you literally live in a cardboard box I don't see why you couldn't make it work.
I've dealt with a very similar situation though OP. Don't wanna go into details but a lot of the traits seem very similar to the guy I was dealing with. Especially the whole commenting on her size and protecting them and acting like he has to be the man of the apartment. The toxicity will just get worse. I'd personally go and talk to him. Knock on his door until he answers, stay until he'll talk with you, and resolve it, with your GF and the landlord there if possible. If nothing changes, she should bail. It sounds like the LL personally knows him through family/other friends by those texts, and I wouldn't' be surprised if she continues to extend him multiple chances.
Don't touch the guy though, or expect a nice assault charge. These guys love to act ready to fight until it's them who gets hurt.
i don't really see misogyny here, he's just being obstinate.
if he wants a in person dialog i'd say hash it out?
My experience with these types of guys is exactly the same. They'll swear up and down that they won't talk on the phone/text, want to talk face to face. But that's because its the place where they can control the narrative, control the environment, and can make excuses. They can walk away, claim they didn't hear you, make excuses. Phone calls you can't really do that. Text there is proof (case in point, OP's screen shots). You can show other people their true self, but not when its a one on one session.
Classic gaslighting and maniuplation.