I started with Apple support and two hours on the phone. They told me there was nothing they could do. That's why I wrote to Tim Cook next, and a member of their executive team called me the following week. There is nothing else I can do to escalate this with Apple now.
Yes, I have a receipt from the UPS store. I dropped if off in person and have a physical receipt. The issue is that Apple claims that the watch they received is not the one I claimed to have sent. Someone swapped it on the way to the service center or on the way back.