On a whim, I tried an idea with the scrollball to see if it would help.
I applied a fair amount of ordinary spit to the scrollball (basically I licked it a couple times), and then did the standard press-down-and-exercise-the-ball method. This actually seemed to shake things up in there a little, so I licked the ball again and did it some more, with a bit more spit this time. Hmm, didn’t help as much, so one more generous lick, then flipped the mouse over, pressed the scrollball down onto a clean sheet of paper and rolled it around a bit.
That seems to have done the trick, for now. Hopefully the fix will last for more than a couple of hours.