I haven't gotten any replies to my questions, but as I've studied I've been able to resolve my problem. My freezer is now running correctly with the compressor stopping once the freezer reaches about 0F.

The solution was simple - the temperature probe of the thermostat is a long wire. This temperature probe inserts through the isolation of the freezer via a small tube. In my case the freezer had been transported about 100 miles and this tempature probe had vibrated about 1 inch out of place. It was still in the tube and appeared ok, but the exposed straight wire was my clue. The rest of the temperature probe wire was coiled. I pressed it back into place and my problem was solved.