Good explanation of Miller. The very limited holding of that case was that it is not within judicial notice that a shotgun is a weapon that could be useful to a militia. That seems to be a very easy standard for a defendant to meet.
I would prefer to think that it is a very difficult standard for a prosecutor to meet.
Even if one were to grant the Supreme Court the power to rule that there are some arms that are protected and others that are not, it would be yet another reach to suggest that it is a burden on a defendant to prove such a distinction in a court of law.