I think you both are on to something.
Tim, we did indeed create the quizzes by duplication. That explains why in my mind, I keep thinking that the Question Bank has something to do with this, but you've helped me make that mental connection.
Emma, I have not manually deleted the cache. I have used Moodle's clear cache menu command, but doing a manual cache clear is an excellent idea.
I'm going to clear the cache now and build one of the quizzes from scratch to see if that fixes things.
Thank you both!