Replaced 'Thermostat' OR replace 'Thermistor'
Thermistor is the temp sensor attached to fin in food compartment.
Thermostat uses the thermistor to control heating sources for cooling process.
'Limp Mode'
When a failure of the temperature sensing device or associated electronic circuitry occurs.
If this should occur, the control system will operate on the energy source selected via the control panel.
The cooling unit will run continuously on the selected energy source.
The refrigerator will continue to operate in this mode indefinitely or until a new sensor is installed and the system is reset
Temp sensing device.....thermistor
Electronic Circuitry....lower circuit board
What TEMP SETTING are you using?
Same 'freezing' using electric and propane?
So IF you replaced the 'thermistor' and it is correctly attached/placed (far right fin...mid position/tip just protruding out top of clip) and functional then Issue could be with the circuit board
Test thermistor.
Unplug leads from lower board (P2 connector)
Place end of thermistor in glass of ice/water....mostly ice
Use thermometer to read temp......33*-35*F...wait 10 minutes
Then measure resistance at leads. 8K-10K Ohms good