Very scary!
Ajoknoblauch's idea to carry a receipt sounds like a good idea. Although the receipt from your bank does not prove that you brought the cash with you to BsAs. A similar idea, with the same problem, would be to record the serial numbers. But those two things might help you to get some reimbursement from your home owners insurance policy. Probably a long shot.
I cannot think of a good defense - other than paying an exchange rate premium. Were customs to take cash from me I would certainly ask for a receipt with serial numbers. But I doubt that you could force a receipt from them.
Bob