Anybody know whether anything like this would work?...
Treat the credit card used as though it were a stolen or lost card -- after all, these crooks now have the number and apparently can charge to it any time they want, just like a stolen card in the real world. You no longer have control over who places charges on it, or when, so it really is no longer in you control.
Call the card company to report the card as stolen or lost (your choice) as of the date and time it was first charged by these guys. Card company may require you to f ile a police report for stolen -- fine, so do it. The scammers are committing fraud at the very least. This gets local law enforcement involved, or at least annoyed.
Card company should immediately cancel that card number, and issue you a new one with a new number. You're without that card for a week or so, but Kevin can't steal any more of your money from it.
I can't say whether this tactic would work, but can tell you my similar experience.
My card number was compromised online earlier this year, completely unbeknownst to me. The idiot who stole it started charging weird things and having them shipped to *me* (real Einstein, this one). But before they started arriving, the card company noticed the abrupt change in my spending pattern and called me to check on it. Results: card number cancelled, new one issued, all charges charged back, merchandise returned, lost money re-credited to me.
Can't hurt to try.