It isn't such a big leap. The Miller case ruled that the 2nd protected the right to own weapons that contribute to the effectiveness/efficiency of the militia. Miller himself simply didn't provide evidence that his saw-off did so (the lack of "judicial notice" cited in Miller). While full autos didn't exist (except in a patent office in England) at the time of the ratification of the 2nd, technology changes and the Constitution's protections grow along with it. No, that's NOT an argument for a "living Constitution," it is an argument for not restricting basic rights because technology changes - that's IT. Just as the 1st Amendment protects speech printed on high-speed offset printers and copying machines nowadays from government censorship, so does the 2nd protect full autos (at least those carried by the average infantryman; crew-served weapons are a different argument for a different time).
So let's summarize my thinking:
If Parker says (after being upheld at the USSC) that wholesale bans on classes of weapons are prohibited as violative of the 2nd Amendment protections of the individual RKBA, and if Miller says that weapons which contribute to the effectiveness/efficiency of the militia cannot be banned, then all that is necessary to reach the conclusion that full autos cannot be banned from ownership by the general population is 1) a violation of that right, which is embodied in Section 922(o) and the '34 NFA and 2) providing "judicial notice" that (for example) an M-4 does indeed "contribute to the effectiveness/efficiency of the militia."
Oooh, let's not. Way too much like a trip down the rabbit hole.
You're asking the U.S. Supreme Court to make a choice, correct? Either an individual right or a collective Militia right.
Yet you expect their answer to be an individual right protecting collective right, Militia-type weapons. Where do you come up with this? The Mad Hatter? The Cheshire Cat? The Queen of Hearts?