The NFA would likely be considered one of the longstanding gun regulations that both Heller and this case say are Constitutional.
Perhaps, but....
New York's Sullivan Act predates the NFA by nearly 30 years. Wasn't that shot down by the NYSRPA decision?
I hope I'm wrong, but I think that approach would be seen as being too literal by the court. The language in bold, that was first used in Heller and was reiterated in Bruen, seems to describe most of what the NFA does:
"[N]othing in our opinion should be taken to cast doubt
on longstanding prohibitions on the possession of firearms by felons and the mentally ill, or laws forbidding
the carrying of firearms in sensitive places such as
schools and government buildings, or
laws imposing
conditions and qualifications on the commercial sale of
arms. [Footnote 26: We identify these presumptively
lawful regulatory measures only as examples; our list
does not purport to be exhaustive]."
Parts of the NFA might be subject to attack, but I think the Court was signaling that existing federal laws like the NFA are in the clear.
