Section 13. That a well-regulated militia, composed of the body of the people, trained to arms, is the proper, natural, and safe defense of a free state; that standing armies, in time of peace, should be avoided as dangerous to liberty; and that in all cases the military should be under strict subordination to, and governed by, the civil power.
This is an angle that I haven't heard before, probably because it's not convenient to either side of the gun debate. The primary purpose of Section 13 (and possibly the Second Amendment) was not to facilitate the overthrow of a tyrannical government, it was to avoid the rise of that government in the first place by preventing standing armies. This also gives the phrase "well-regulated militia" a bit of a clearer meaning. In order to make sure that standing armies are unnecessary you don't simply ensure that every civilian had access to guns, they also had to be capable of fighting together as a well-regulated militia.