Q: Multiple Apple IDs and verifying e-mail - locked out

I have two apple ids under one email address:

One I created years and years ago, which is a single, non-email name that is associated with an e-mail address.

I have an additional apple id which is the e-mail address that is used in the account above which apple made me create when they converted to the e-mail address as apple id requirement.

Now, I have been locked out of either account. During the recovery process, iforgot requires me to verify the email address while trying to sign in to either account. When I try to verify, I will receive the code, but then after I enter it and hit verify, iforgot will present me with an error that the email address is used on another account.

Now I have two apple ids that I cannot use or modify the e-mail address of because either one can be verified.

Any suggestions or help?