I have no experience of that company but I am struggling to comprehend why you left your wallet in a bag that was being gate checked. That's just asking for trouble. I can only assume it was oversight rather than a conscious decision. Presumably BA gave you a baggage tag / receipt when they took your bag from you to check it into the hold? You should have simply filed a missing baggage report with World Tracer and then your bag would have been found and delivered to your address in the USA without you having to pay $426 in charges and import duties etc. At least you didn't leave your passport in your bag too! I suppose that's the only saving grace here.
Oh, and welcome to FT