Can't log out of old iCloud account?

I have a bit of a unique situation and I'm not sure how to go about fixing it. I'm using my boyfriend's old iphone since he got a new phone. I've been using it for several years now. I never had an iphone before so I didn't know at the time that he was logged in on his account, so I just went about using his phone without him ever logging out. He gave me his password if I wanted to download new apps and whatever. Now I've made my own apple ID so I could use it for a new ipad I got and I wanted to switch the phone to my ID as well so I could find it if it was ever lost of stolen. He's totally fine with this. Except that now I can't log out of his account on my phone under icloud so I can put my new ID in. Not sure what triggered it, but his account is locked now (maybe me logging in on a new account on the same phone?). We can't seem to recover his account because it asks for his birthday and his actually birthday is apparently not the right answer. He doesn't know what he put down for his birthday when he was making the account apparently. You would think we could have an email sent to his email address to recover it, but apparently the one he used is an old email and he can't access that email now either.

Should I just call apple? Would they even unlock his account if he doesn't know what he put for his own **** birthday? Has anyone else dealt with something like this before?

Thanks for whatever help anyone can provide!