I'm soaking up the info in this thread for sure.  I always just assumed the simple deform modifier was broken, and never used it.  I remember reading somewhere once that the simple deform was one of those modifiers that was created when Blender was first made, and that the way it works was never updated since then, and so the modifier itself was outdated and irrelevant now.  I can see from what's going on here that this was the wrong assumption!