This is an interesting an unique situation. I did read my warranty information that specifically states that DJI can and may replace a damaged drone with a new or refurbished device. For the majority of us, this is not an issue as the replaced device has the same warranty coverage. Even with DJI care and refresh, the repaired drone has the serial and gimbel number transferred to the warranty coverage.
From what I can see, an N number registration is assigned to a serial number. With the new drone, the serial number does change. For what it's worth, I can see an analogy of a plane being damaged and the insurance company buys you a new plane. You have to register the new plane.
I do not believe it is cost effective for DJI to repair a drone. Actually, i would be more worried that someone removes and replaces every component in the drone back into a new case by hand. If you have ever opened a drone, you would see a rather circuitous maze of glued wires routed through small opening and tight tolerances. This is all done by machine and to reproduce it by hand is technically demanding.
So, I appreciate your unique situation. I do not think you're response to DJI is valid. The item has not been stolen and I doubt any law person would respond. Plus, DJI is a private corporation. There is no board or responsible corporate entity. I would contact the FAA and see what the options are. And it's not lying to the FAA to say a drone was repaired and the serial number changed. See if they can do a transfer of the number. From what I read, that's about $10.00
If it were me, and as frustrated as you, I would insist on speaking to a DJI service rep. Then, I would file a complaint to the BBB. You might get a faster response by filing an online complaint with the State Attorney general, dept. of consumer fraud. A call from them always gets a response.
