SCOTUS also ruled in United States v. Cruikshank that the First Amendment right to assembly was not intended to limit the powers of the State governments in respect to their own citizens. Reaching back to a case before SCOTUS began enforcing fundamental rights protected by the Bill of Rights doesn't really carry much weight these days.
United States v. Miller could also be read with "reasonable relationship to the preservation or efficiency of a well regulated militia" indicating that the "arms" most protected by the Second Amendment are those which are in use by the military. After all, how can the militia get training in use of those weapons if they are not available for use?
The actual text from United States v. Miller of "The Court cannot take judicial notice that a shotgun having a barrel less than 18 inches long has today any reasonable relation to the preservation or efficiency of a well regulated militia, and therefore cannot say that the Second Amendment guarantees to the citizen the right to keep and bear such a weapon." seems to support the position I mention above at least as well as the one you put forth.