> We’ve resorted to just cancelling the order quietly once we find out, without informing the fraudster. When they invariably call an hour later inquiring about their delivery (with a voice totally not matching the name), we either tell them we’re sending cops or cuss them out loudly. The silver lining is that it’s fun to witness their reactions on the phone when they realize they’ve been caught.

Don't do this. Just give an automated message that you've canceled the order due to being unable to process their payment, without elaborating on what was wrong with the payment. If they call, give them the same information and nothing more.

Every piece of additional data you give them about how your anti-fraud system works helps them to evade it. Also, as you grow, speaking to them on the phone will become a larger and larger risk as some fraudsters will be very skilled at convincing your customer service people that they are legit.