Answer: Sony should have returned your camera by FedEx with a signature required, and when it got lost, it should have taken the matter up with its shipping company — not asked you to pester the shipper for the package.
As far as I can tell, your entire correspondence with Sony took place by phone. I find that problematic. Had you emailed Sony, your request would have been assigned a case number and you would have a clean paper trail (or in your case, an electronic trail) that documented your queries and its responses.
But when you call Sony, only the company has a record of the conversation. That puts you at a disadvantage when you’re trying to resolve the case.
Appealing to a supervisor was a good instinct, but why not ask for the supervisor’s email and get the response in writing as well? Again, when only one side is recording the call for “quality assurance” purposes, it’s your loss.
The only way to stop this game of corporate ping-pong and escalate your case is to start moving up the chain of command at Sony, starting with an email through its site. (Here’s a tip: If your email goes into a black hole, try an electronic chat. You can easily copy the back-and-forth for your own records.)
If that doesn’t work, try sending an email to a supervisor. Here’s a a list of Sony’s executives. Most email formats are firstname.lastname@example.org (and sometimes they add the division, like @playstation.sony.com).
I contacted Sony on your behalf. The company agreed to send you a replacement camera at no extra cost.