I'm fairly certain that the ATF would allow you to disassemble the gun and give them the receiver. The parts kits for many of these guns are quite valuable. This WWII collector who's an FFL that me and my friend both know from the gun shows supposedly did that years ago. He is a standard FFL, not a class 3 however.
The story was that he had an old woman hand him a MP40, and he gave up the receiver and kept the parts kit. I think he also got a parts kit for a MG42 the same way. I should ask him the next time I see him...
I can't see why they'd want to cut up all parts, such as the barrel or trigger etc when they are available anyway. Now of course the receiver, thats different.
Winchester 73, the TFL user that won the west