I remembered during lunch that I read somewhere (here, I'm sure) that OOTP treats "true black" (0,0,0 RGB value) as transparent. So I went in to Paint Shop Pro, figured out how to use the color replacer tool, and changed all the 0,0,0 black to 5,5,5 "black". Voila. Problem solved.
I don't know if it's the "recommended" method, but hey... it worked.
