I called and asked for advice...
The first attempt was to change the water inlet valve. That was a fairly complex but inexpensive repair, but it was not the problem. I called back and after a few minutes on the phone with support, we were able to determine that the ice level power control board was the culprit. It was a little on the spendy side but was a 10-minute job and now it works like a champ!
Thanks appliancepartspros!