I wonder if you are in Europe or somehow related? Would anyone know of any success case where you can GDPR them to receive all the data associated to you in this way? It's not "your account", but at least might give you your data back.
Just because you've lost access doesn't mean your gmail doesn't continue to receive emails, and if those emails are considered personal data, what stops you continuing to send data access requests to help yourself migrate?
What should be possible, though, is to migrate your account without access to your email. For example make the user save a special TOTP secret that will be used only for dangerous actions and not just for logging in.