[skimoose]

We've been powering the camera via the backup battery directly - should be enough (according to 2 different manuals/spec sheets I've seen, 7.2V should be within spec for the camera.). We've tried 2 different batteries (one new, one from last season.) Whenever one fully charges (LED on charger turns green - does that indicate full charge?), we just switch them out. Am I doing things right?

Yes, you're charging correctly and the backup battery will work. However, when we were testing the camera last year on the backup battery, with the servos for tracking, the usable battery time was not that long. I don't remember exactly how long, but it was short enough for me to note that we'd be changing backup batteries after every match to play it safe.