After defrosting the freezer, removing the mound of ice on the connector and inside the motor housing, I removed the one screw holding the icemaker in place and removed it. I also removed the motor housing below it and cleaned the ice out of that. After reinstalling them, it soon became clear that the same problem remained. With all the excess water, I counted on there being no blockage in the H20 feed lines and that the valve was OK. So I ordered a new icemaker.
Removing and replacing the icemaker itself was only a 5 minute job, involving the one phillips head screw securing it to the left wall of the freezer. Defrosting the freezer and removing all the excess ice from the leaking maker was the time-killer.