Hmmm.
Miller is historically illiterate. Under the Second Amendment the ONLY weapons protected are combat arms...
Ironically, as I recall, the case making that distinction is referred to as “Miller”.
Cue Alanis Morrisette. That was the one thing United States vs Miller did rule.
While this was the decision in the Supreme Court's 1939 Miller decision, I don't think the Heller decision is consistent with that narrow reading.
The Heller Court adopted the "in common use" language but also established that the right to keep and bear arms pre-existed the Second Amendment and that the right to defend one's self in the home is part of the pre-existing right. By implication, there would be no reason to insist on a militia purpose for arms suitable for self-defense in the home.
Protecting one's hearing by the use of a "silencer" on a home self-defense weapon ought to be protected by the Second Amendment as well as the use of a short-barreled shotgun.