I installed my brake and brake lever last night, and it all worked as advertized. It is very strange, but it makes sense, somehow, when I watch it work. And it works well, though I found out that my brake reach is too long, so stopping power is pretty lousy.
Anyway, what I realized (as most of you probably know) is that it's not "You have to slow down by using the pedals!" (negative connotation), it's "You can slow down by using the pedals!" (positive connotation, and amazement). So I'll fix the brake at some point and just use it as a helper for now. It's great to be on that bike.
Thanks everyone for all your help.