well they have to check the logs to confirm that it happened, so you need to at least be able to give them an approximate date. And let this be a lesson to always handle important items more carefully and slow down when moving them around. It's pretty hard to drop an item you intended to use that's rare ex since the confirmation prompt requires you to press a different directional button than you used to select Drop in the first place.

The policy is strict to prevent abuse of it. SE has always been ultra hands-off with its support staff. I'd try to contact them again and make yourself a stronger case (After all, you can only ever have one at a time, so there's no way you could get a duplicate...) and if the GM won't help, make another call and ask (politely) for escalation to a SGM/LGM.