Haven't seen a controller (STC type) that hasn't got run on protection. You only need 5-10 minutes to let the compressor rest.
What I was saying about the probe location, if you think about it will make sense. This isn't a fermentation fridge where the ferment is producing heat, its just a storage space that is kept cold.
Any heat is entering through the walls/lid/floor, to heat up the water in the bottle the air temperature has to be hot enough for long enough to trigger the controller to turn on the compressor.
Remember that the temperature of beer is going to go up and down about the same amount.
By just measuring the air temperature, yes the compressor will come on more often, but for a shorter time. As the air temperature is kept in a narrower band the temperature of the beer will be much more stable just due to its thermal mass.
Any issues with the amount of dissolved CO2 will be minimised.
Again that presupposes that you have a fan in there and the air is kept fairly homogeneous.