Unable to change my apple id password due to dead email on file

I never bothered to migrate my old mac.com email because I never used it. I don't know the answers to my security questions because they are too vague. What was your first car? I am faced with make model year XL signifier etc Best friends name? full, nickname, first .... I never wrote any of this down.

But all of that is besided the point.

I have a funtioning apple ID with a active email that it recognizes and a password that works. But I can't change the password without the dead email because that is where apple is sending the instructions.

How do I fix this? Is a genius bar trip?