Just an update from me . . .
Yes, this problem has all the hallmarks of a signature error, but all of my work for the last few years has been on the same PC and in the same file environment.
Last night I released a second app to see if the problem repeats. I had taken this app out of production last year so it was something that I could release quickly with no risk. It comes from the same PC and file system so is a good rerun of the previous release path. The app will be a few days in review before I can see the results.
Meanwhile, no change on my earlier release. I have put a note in the release notes advising users to uninstall their previous version, but I don't expect many will see it. Otherwise the update seems to just sit in the Playstore queue in a "Pending..." state. I have left one of my devices in that situation to see if that ever changes.