So, yesterday evening, with everything apparently working, I clicked on the updater thingie on the Kubuntu laptop, and, after applying sundry updates, it helpfully offered to do a dist-upgrade from Extenuating Earwig to Flustered Flamingo.
It took overnight plus various responses to prompts. When all was said, done, and rebooted, it was working... except... my USB serial port was spontaneously disconnecting.
One quick Google got me to this page; removing brltty - and why would I want my serial ports to speak Braille, anyway? - indeed solved the problem.
The background pattern in my Gtk window still isn't showing up on that machine, but it's not like that's essential to the function of the program at hand.