mneme_forgets pointed out my error. Being a stubborn little wench, I had to go and research the matter to assure myself that she was correct.
I found an amusing blog entry on the subject which I'm preserving for future reference. I like the way this person writes.
Note to self: sooner or later, I need to hammer out my use of "which" and "that" once and for all, and decide whether I'm going to follow MLA or APA format for quoted phrase + comma/period.