There's a decent amount of credible advice on troubleshooting refrigerator problems on the web, and after several unrelated sources suggested that the symptoms I was seeing were likely caused by a bad main control board and probably a freezer temperature sensor I decided to replace both. I think it's a good idea to avoid taking any single web site's advice if possible.
The main control board was very easy to replace - just read the instructions carefully because some models require snipping a wire on one of the connectors and also one on a connector down near the compressor.
The sensor was a bit tricky to replace because once you cut the old sensor off you don't have a lot of wire to work with - maybe 2". Be prepared with some small butt connectors, the size I used was for #22 - #16 wire. Also, one tab on the plastic sensor cover broke when I was removing it, so if you're a perfectionist you might try removing that before placing your order.
My time estimate includes web research and troubleshooting - installation time was about 25 minutes.