Still no joy and a (vague) new theory
Thanks to themacwizard who reported success after he
deleted all items belonging to either MobileMe or Me.com and then quit Keychain Access
Upon seeing that, I immediately went to try it, but it turned out I had no Keychain items associated with MobileMe or Me.com so I couldn't delete them.
FWIW, I was recently at the Apple Store in Grand Central Terminal and, having time to spare, thought I might try to get a quick Genius Bar appointment and discuss this problem there. Unfortunately, it was late in the day and there were no slots left, but the (non-Genius) store employee I was talking to asked what my problem was. When I told him and added that I
could connect to iCloud from a newly created account on my Mac, he said that suggested "corruption" in my main account. He said if I brought in my Mac they could fix that for me. However, he didn't explain the nature of the corruption or what they would do. I haven't had a chance to follow up on this yet, although I plan to.
In the meanwhile, has anyone here ever heard of this explanation and solution?