What to do when Apple account recovery doesn't call?

We have initiated account recovery three times for a relative's iPad.

Each time, we received an email that Apple would call us at a specific date and time. Then nobody called.

We have access to the phone number and email account associated with the Apple ID. We don't have access to older devices or past passwords.

We went to the Apple Store.

Apple Store told us account recovery is automated. Apple store put us back into the same process.

We are locked out of our account. Apple fails to call at the time indicated in emails. We are stuck in a looping failure of customer service.

At this point, we have been locked out of the account for 6 weeks. Each time, Apple says via email that someone will call in 2 weeks, then nobody calls.

Apple support can't help. Apple stores can't help. There is no number or email to call, and Apple fails to follow through on calling three times in a row.

So what am I supposed to do? I just want to be able to add new apps on an iPad?