[Nate the Great]

Actually, this whole business of "six coordinates can handle everything" needs a little scrutiny by itself. I propose the following:

1. The galaxy is 100,000 lightyears across.
2. The galaxy rotates around it's center in such a fashion that it can be taken as read that it's standing still, with some line (say the one going through Earth) taken as a "Prime Meridian."
3. Use some form of polar (or rather, cylindrical) coordinate system makes more sense, as I believe that planets get denser as you head inward and sparser as you go outward.
4. Hence three coordinates: angle, distance, and elevation above or below the galactic plane.
5. For gate address 123456, 1 assigns the angle to a range 1/38th of the circle, 2 assigns the angle to a range 1/38th of the previous, or 1444 slices of pie, so to speak. 3 assigns a broad radial band of 5000 lightyears, 4 assigns a narrower radial band of 300 lightyears (all of this is rounding, of course). 5 and 6 assigns the height above or below the galactic plane (I can't assign numbers because I don't recall the galactic height offhand).
6. Within each of these ranges there is precisely 1 Stargate. Or rather, one "active" Gate. This is similar to some of the Star Trek games, where a "sector" is defined by the major planetary system within it.

Actually, by this system I think you'd need another coordinate for the radius to make it work. But at least it makes more sense than the old "box connected to Earth" routine.