Well, there it is. I had a strong suspicion about that interpretation, but it's informative to know that.
I can't support this kind of change to the 2nd. Under that definition, the states get sweeping authority to decide who is allowed to own a weapon, which probably only extends to the police and National Guard units. Klein, I just read your comment about updating the style of the militia groups in order to justify this kind of change and I really like those ideas but I have little faith that most state governments have the foresight to see it this way. Instead, I think a step in the other direction would be probable - outcry from the general populace, followed by a few high-profile crackdowns that drive the unrecognized militia groups further into the shadows along with a bunch more people who, unwilling to give up their firearms, will be more inclined to align with these newly-outlawed groups. The end result would be a huge increase in distrust of government combined with further isolation and possible radicalization of many otherwise law-abiding citizens who now have to make a perceived choice between legality and their constitutional right. These five words don't just kick a hole in the 2nd amendment, they raze it to the ground and shatter a significant facet of national culture in the process. Hyperbole? Possibly. But a great many people will see it this way. Those sorts of instantaneous changes are typically met with open hostility.
The militia membership idea is a super cool one. Regardless of whether or not any changes are made by the ATF, legislature, or Supreme Court, we ought to encourage active physical participation in local community organizations such as what these would be. I'm not so sure about the governmental oversight you propose, although for the extra goodies like reliable org charts and reserved frequencies it would likely be necessary. Some limited method like a county coordinator, or checkups from the Guard or something may work. Isolation appears to be a common factor in a great many of these shooters' backgrounds, and an atmosphere of isolation is getting continually easier to maintain. On the other hand, gang violence (which is a much more frequent source of gun-related deaths) seems to occur mostly in groups, so there's that counterpoint. It does seem that we are less enthusiastic about civil service that the romanticized past, and gun club militias may be one way out of that slump. You just need to make sure they don't swing either towards paramilitary political groups, or jumped-up gangs.