Q: Reset Apple ID without security Q's or Email

I am writing on behalf of my Father who has an iPad 2 not updated in years. Incredibly he has managed to forget his password, the answers to his security questions, the recovery email account password, he never registered card information and bought the iPad from eBay so has no proof of purchase.

Frustratingly it looks like its impossible to restore the iPad without the Apple ID password and impossible to reset the account without some combination of the information I've mentioned above.

Is there anyway around this problem?

Thank you,

Chris