"This model fridge has a thermostat screwed into the roof of the refrigerator. It is not adjustable since it is not on the coils".
Explain this. Are you talking about the rear FAN tstat or the tstat that controls the interior refer temp? The rear fans, the tstat should be mounted to the upper condenser fins. The INTERIOR tstat is NOT mounted on any part of the roof of the refer. Your problem may be as simple as making sure the upper outside ventilation door, the area INSIDE has no gaps or dead air spaces to allow hot convection air to not flow out that door but stay inside. BOTH rear fans are running? What is the AC voltage to the unit? Should not be below 110. If it is, then 120 operation will not be as good. Have you tried on LP for 24 hours? Doug