Well, now, there is the answer on how to balance the QR right there! Make it work just like the, uh, what are they called? The things that generate supplies from solar power (read: per star in system). IIRC (which should rightly be called into question, after all, I was wrong about the QR!), the Solar Panel thingymajigs act as I described, and I see no reason for the QR to act differently (or bases, for that matter!)
Hell, while we're at it, you could almost accomplish the same thing by modding the QR to have an obscenely high Solar Panel Thingymajig ability. Of coarse, then Black holes and Nebulas would mysteriously cause the QR to stop functioning....
Oh well, just a thought.