It's really too bad that Miller and his Partner weren't big time gangsters, even at the level of Bonnie and Clyde. If they were ,they'd have had Thompsons or BARs, or both. Even the Supreme Court would likely have ruled that it was permissible to "take judicial notice" that those were suitable for military/militia use.
There was already evidence, though none presented in court, that a sawed-off shotgun has military application. "Trench guns" were used during WWI and, AFAIK, were in the Army's arsenal at the time.