Yeah, I'm pretty sure my semantics are off... I really am just getting into bikes and am still struggling with terminology. I've learned my other hobbies (computers, cars, photography) very gradually, but never paid attention to bikes until I realized I was actually starting to enjoy riding beyond just getting to class in less time. So I'm having to learn all the terminology all at once.

The chain did come off the rear as far as I can tell. I'm running a front derailleur and it's adjusted properly and the shifter (yes, friction) is tightened so it can't move. I had problems at the front when I first put on the chainring, and I adjusted it very carefully, so I'm pretty sure that's not the problem. The issue is that the chain fell off when I was really going fast, so by the time I looked down, it was off both the front chainring and the rear sprocket.

Would the limit stops really help? I'm not sure I understand exactly how they function -- I thought they limited the range at the outside edge of 7th and the inside edge of 1st?

FWIW, I believe the chainline angle is such that the way it fell off (towards the outside on the sprockets, and towards the inside on the chainring) would be counterintuitive if that were the issue.