I had to recover my Apple ID recently. All I needed was the recovery address and my date of birth.
You're a little vague on the ID theft allegation, but the harassment can be stopped by blocking mail from that source. I don't think Apple has any obligation to help you with this. Allowing unverified people to disable accounts, would be a more serious problem than the occasional lost account.
One place where I can sympathize with you is the ridiculous password requirements that Apple has. They are definitely creating a much higher percentage of forgotten passwords than other secure services I know of.