OK, I got a letter from ATF FTB matching the ATF posting at the ATF website FAQ:
(Paraphrasing) An original Mauser Broomhandle is a curio and relic, and may be owned legally as a pistol with an original shoulder stock or an accurate replica of an original shoulder stock.
A new broomhandle pistol build on a new frame from an original parts set is a new pistol, not a curio or relic, and must follow all NFA rules: an original shoulderstock or repro would constitute a short barrel rifle SBR and require federal registration.
And if I read the regs correctly, an original Mauser Broomhandle pistol with a new shoulder stock that is not an accurate replica of an original would constitute a SBR under NFA.