Resolved!

First, I want to thank Locopon (Mauricio) for helping me try to figure this out. We've exchanged lots of emails trying to understand what was happening.

In parallel with working with locopon, I had opened a ticket with my hosting company - PowerDNN - to ask if they knew anything about this issue. They initially replied that they charge an hourly rate to work on custom modules but after I pointed out that this comes with the core DNN installation that they installed when they set up my site in the first place, they agreed to take a look. I created them a guest account so they could recreate the problem. They just sent me a note saying they fixed the problem. They said there was an older version of a .js file that was causing the issue. I just checked and all is well.

So, thanks locopon. Sorry it was a wild goose chase on your part. Kudos to PowerDNN for digging in and finding a relatively obscure problem.

Tom