I simply used the joystick to raise and lower the Z a couple of times. The drift stopped after that.
My interpretation is that the controller was sending (or the received was receiving) supurious “down” signals. However, this does not explain what happened while the job was running - I would have expected the joystick input to be disabled while a program is operating. I’m going to run some experiments machining air and see what I can find.
It’s too bad that the controller does not have an “off” button because it would be good to simply make that part of the pre “go” checklist “turn off controller” and see if that stops the problem.