Chris, thanks, but that didn't work. There may be a bug in iTunes, but I think the problem began in setup when I okayed syncing with iCloud. That seemed to cost me the ability to manually manage music. I tried changing that in iTunes, and it appeared to accept the change, but I still couldn't bring up the option on the Summary page from "Manually manage music and videos." It only offered "Manually manage videos," which was not consistent with Apple Support's step-by-step in HT1535.
I took the unit back to factory defaults, ignored the offer to use iCloud, and got what I was hoping for: an offer in the Music tab to sync "Entire music library." That did it. I appreciate your weighing in.
Michael