I'm not entirely sure there is a distinction between arms vs. ordnance in the 2nd Amendment. That question has not been tested, explicitly, before the court, AFAIK, but I'm sure I'll be corrected. What the court has said is that “the Second Amendment extends, prima facie, to all instruments that constitute bearable arms, even those that were not in existence at the time of the founding.” (Heller)
Muzzle-loading cannons are not considered firearms in the US and are therefore not regulated by the 1934 National Firearms Act (NFA). BUT, muzzle-loading muskets are also generally not considered firearms under law. So, we're forcing modern definitions of terms and how the NFA defines terms onto the 2A's terminology. And that may not be proper. Heller and the subsequent Caetano cases may both provide some guidance here.
So both firearms and muzzle loaders (in modern Federal regulation) would certainly both fall under the 2nd Amendment. By extension, the question would be whether other forms of arms (defined as destructive devices in the NFA) fall under the blanet of "arms" under. 2nd Amendment .
And, even if they did, "reasonable" restrictions are apparently permissible for the Court (Heller, again). So, the NFA terminology - which creates restrictions in and of themselves - could fall under the fabric of "reasonable" restrictions to the right to bear "arms". The Court does allow restrictions on arms that are "dangerous and unusual"
This has not been fully tested in the courts, but "arms" may mean any weapon that could be
individually borne. NFA distinguises between "firearms," "destructive devices," and "any other weapons." All would seem to be "arms." Perhaps this is not directly germane, but remember that missiles, nuclear weapons, and other devices fall under the rubric of "arms control" treaties.
In short, what I'm arguing is that the conventions and terminology created under the NFA and other regulation does not necessarily correlate with the term "arms" under the Second Amendment.
The First Amendment never defined technologies - if it did, "speech" and "press" would mean podium oratory, printed and handwritten matter, and leave open the question of whether the Internet, TV, radio, cable TV etc were protected under the First Amendment. Of course, that is not the case, and the terminology has adapted to the times.
Similarly, the Second Amendment is not locked into the "arms" of 1789 (muskets, cannon and swords). The term "arms" is adaptable, and evolves with the times. Witness the Caetano case (2016) where the Court strongly leaned towards the view that stun guns/tasers fell under the Second Amendment, because they are a form of "arms," and should not be banned outright because they are not "dangerous and unusual".
The militia clause is not particularly troublesome, and arms are different from ordnance.
That said, you can, in fact, buy decommissioned fighter jets, tanks with functional main guns, artillery pieces, rocket launchers, etc. These are destructive devices, and it's the same $200 stamp as any other NFA item (more processes to actually use an aircraft in regulated airspace, obviously) Of course, most of us can't afford the $300K+ for an operational M60 tank or ~$5M for a fully functional MiG-29.
You could also build and register a state-of-the-art fighter if you had the means. Remember, the extreme majority of military weapons and other hardware are developed, tested and produced by civilian entities.