O.K. Problem solved. After much head-scratching and floor-pacing, I decided to bypass epubcheck and run it by this validator:
http://www.w3schools.com/xml/xml_validator.asp
(Thanks, Liz Castro, for the referral.) It pointed me in the right direction. I did have some xml issues, but not the one epubcheck was claiming. Anyway, everything's cleaned up now, and I'm looking at a validated file.
(I still want my money back for CS5.)