I have resolved the issue. It took a good deal of digging, but I finally tripped over something in /var/log/messages that got me thinking that the error dialogs note that my home directory didn't exist might actually be telling me that it existed, which it does, but that I somehow lacked permission to read it. Sure enough, I had SELinux enabled and in enforcement mode. I don't know a thing about SELinux. I don't know how I managed to get it turned on. But, once I turned it off my world became sweet once again.
