In these cases go directly to your bank or payment card provider (Visa, MasterCard, etc.). You usually have ~6 months from the day of the purchase to make chargeback request.
Just sign up with a different card. As a matter of fact, if I ever did a chargeback I would probably insist I get a new card number and maybe consider changing my address with the bank to be slightly different (maybe spell out "street", use my full zip, etc.). Might not be enough, but clearly Amazon doesn't care much about detecting fraud. And, anecdotally, I've had three different accounts over the years with various Prime promos and haven't had a problem.
