Not sure 100% but that doesn't matter a lot, because, the 2nd protects an INDIVIDUAL right which is far broader than the "civic purpose" example given in the prefatory statement. (Which is in and part of Parker, by the way. Have you read it yet?) So at some point (the sooner the better) NFA '34 is gonna go bye bye for being the unconstitutional power grab that it was.
My guess is that Mr. Miller's sawed-off shotgun had none of the above military-type features and would have been virtually worthless in a combat situation. The National Firearms Act of 1934 took the position that if a shotgun had a barrel less than 18", it was probably going to be carried concealed by criminals.