Nice try, I know that is where you desperately want to get. Being a member of the "organized" or "unorganized" militia is only one of several reasons "the right (due to anyone by just claim, legal guarantees, moral principles) of the people (individual citizens) to keep (to hold or retain in one's possession) and bear (carry) arms (weapons, esp. firearms). Name a type of firearm that is not suited to the militia.
The correct phrase is, "has some reasonable relationship to the preservation or efficiency of a well regulated militia".
It's not up to me to say. But I'd say a sawed-off shotgun would qualify -- it's not a militia-type weapon.
The trench gun in WWI was 20" and had a bayonet lug. That certainly qualifies.