Unless he too chose to plea bargain for probation. Then we'd be right where we are. Now if he'd a had a Thompson or a BAR, even a Supreme Court Justice would be hard pressed to argue that it wasn't OK to take judicial notice that those have military utility. By then the Thompson were an issue item, although still not real common, the BAR had first been used in WW-I. Or maybe he could, lots of things are possible when only one side gets to "tell it to the judge", or in this case the Justices.
Which, a few years after Miller, the 1st Circuit Court in Cases thought to be an odd conclusion -- that a private citizen may keep and bear military arms.
However, I don't see any conclusion other than that.