That kinda runs afoul of the “...and bear arms” part of the Second Amendment, doesn’t it? How does he propose to achieve this without such legislation being deemed unconstitutional?
Probably the same way they did the National Firearms Act of '34, the Gun Control Act of '68, and the Assault Weapons ban of '94. All survived constitutional challenges. It's even worse now.
The way I read Miller in light of facts not available to the Court, the NFA did not withstand the constitutional challenge on appeal. The issue on appeal was absence of a finding that a short barrel shotgun had any part of the ordinary military equipment or that its use could contribute to the common defense. If SCOTUS had that "finding," the Miller case stands for the proposition that it (SCOTUS) would have ruled the NFA unconstitutional.
The District Court in fact found the NFA to be unconstitutional in light of the 2nd amendment. SCOTUS remanded the case.
It is most disappointing that 9 of 9 SCOTUS judges got the Miller absolutely wrong in the Heller decision, and there is no intellectually defensible reason for the chronic error.