It took a couple of hours with Apple support, but we figured out the problem. You can see the symptoms I posted in my earlier post. Here's another screenshot showing that there were 2 accounts (a .com and .edu) signed into App Store, Books, and News... and one account additionally listed Music and TV. I wanted to keep the .edu account and remove the .com.

I had been trying to sign out of the App Store, but was receiving the error messages posted by the OP.
I had already gone to the Music app and found that I was signed in with the .com account. I signed out.
Then, during my support call the Apple rep got me to open the Books app... something I don't think I've ever done. Sure enough, Books showed that my .com account was signed in. I was able to sign out from Books and -jackpot- the .com account disappeared from the screenshot above and my App Store went back to being signed into the .edu account!!!