I opened up my Dolphin this morning to get to the innards of the impeller.

Sure enough: a couple of twigs. That was what was encouraging it to stage sit-down strikes with annoying frequency. Twigs removed. Dolphin reassembled and back to work, eager as a beaver.
Meanwhile, still having trouble with my Zodiac pool pump. My SolarEdge solar electricity system seems to be producing too much voltage for it to cope with during the day, so I am having the run the pump at night. Not ideal.
The joys of pool ownership!