That’s a tough one.
From a completely objective standpoint, he’s the one not being a very good friend at all.
So, what I’D do, as to not lose friends in the process, is invite him over one-on-one. Then, when he inevitably starts going off on your girlfriend, start with telling him he’s blowing it way out of proportion (as you said, you’re not at the hugging stage yet, so even if he was right, he’s going too far). If that puts some sense into him, you can stop there (for now). But, if he escalates it further, THEN go into the whole “stubborn, hypocritical, narcissistic” bit. What he does next should tell you what to do with him.
No matter what happens though, I’ll be here for you (in memechat).