I had verified that the water supply was healthy, so it was either the icemaker unit or the water valve. I replaced the icemake first, based on a the pareto showing it was the culprit for most other people, but it didn't help. That replacement was straightforward; the hardest part was reaching all the way back to unclip the wiring harness since I am too lazy to totally empty the bottom freezer and remove the door.
So the next step was the water valve. The hardest part of this was pulling the fridge out from its corner without scratching the floor, and without help from anyone else. Once the fridge was out from the wall and the water supply turned off, it took four very simple steps to demo the old valve: 1. one screw to free the valve from the back of the fridge, 2. unplug the electrical/signal cable, 3. Unscrew the nut on the supply line connecting it to the inlet of the valve, 4. compress the washer and pull out the outlet line that runs from the valve to the icemaker. Installing the new valve took those same steps in reverse order, plus a little bit of leakchecking with the water supply back on. Et voila! Ice!
The total active time was about 10minutes, but I let the machine cycle through making ice to make sure it wasn't leaking when the valve was open and that took some patience.