If ever there was a use-case for chargebacks, this is it. Threaten their support to refund or you will file a chargeback, and then file one if they refuse.
To me, ideally the end result is a chargeback instead a customer support refund. Otherwise they have no incentive to change. A high chargeback percentage could be that incentive.
I think the credit card companies expect you to attempt to talk it out with the merchant first though, so you'd still want to reach out to customer support first to "give them a chance".