Thanks for that advice.
I took off that center plate and found two old (made in usa!) ballasts, one of which was buzzing badly, the other of which I'm not totally sure if it's working because I could only get 1 lane to light up consistently.
I'll test the second ballast more thoroughly today as I couldn't figure out which two lanes went to each ballast, so I was getting confused as I put bulbs in and out.
If it turns out just one ballast is bad, can I just cut it out of the equation? I would think all I have to do is cut the black and white power to the bad ballast, and then cap it off with a wire nut.
Then I could either use the fixture with just two bulbs on the good ballast, or, I could pick up one of those T8 "electronic" ballasts, and run the T8 LED bulbs in them.
Does the fixture work fine with one ballast power line cut?