Please keep us posted as to what happens with your foray into the BATFE. It should be educational. From other reports I have read, getting the BATFE to allow a SN restamping (and I understand that they will specify the new SN, not you) is far from being as simple as sending a request letter.

Case in point, the Bonnie Parker "Squat Gun" a Colt Detective Special. I don't remember the details, but the SN had been removed. The auction house (RR Auctions, Amherst NH) handling the sale went to BATFE to get it approved for sale (knowing it was going to bring a handsome price), but had a very difficult time getting BATFE cooperation. That auction was in 2012. I'd suggest you contact RR Auctions and get the story from them.