I wouldn't think you would have to pull the fridge out to change the thermistor. The snip the tip one is what I had cause problems and had to switch back to the standard thermistor. I thought that's what you had when you said adjustable.
If you don't already have it, you might check here for a service manual for your model. It should give you some ideas about how to test the thermistor.
http://bryantrv.com//docs.html