The symptoms: all of the ice in a full ice bin will melt into one solid block after a few days. An even after dumping out the block of ice last night, the little bit of ice that has been made since then has already started to bond together. Also, I often find condensation on items in the freezer. Clearly, the freezer is spending too long in defrost, or defrosting too often, or both.
The research I’ve done thus far - not for the same model, however - has most often suggested that the thermistor in the freezer is the culprit. So I removed the cover over the control board and found the wires to the freezer thermistor. I unplugged the connector to measure the resistance of the thermistor and got a reading of 1000 ohms in hot (126F) water and 7900 ohms in cold (35F) water. While that does prove that the thermistor is responding to changes in temperature, I have no idea if those values are anywhere close to what they should be, but both this site and Sear’s parts direct have it in stock (6500JK1004A) and it is cheap enough to just go ahead and buy it to see.
However, some of the search results on this problem point to the control board that the thermistor plugs into being the culprit. That is a much more expensive proposition, at about $113 + shipping.
If anyone has some additional tests for me to perform, or can find a schematic (I’m an EE, so I ought to be able to read it), that would be most welcome.