So... I'm stoked!
I have mastered riding on rollers!!
datlas' (I think it was him?) recommendation of having someone hold me was the ticket. We also moved the rollers so that I could rest elbows on a doorframe instead of smashing my hands on them, and that made a huge difference. After about 10 minutes he stood behind me without touching me just to be there, and then a few minutes later he moved away completely and I just relied on my elbows.
Whee!