I am having the exact same situation with my side by side, but my model is kssp36qjs00.
I have replaced the following myself and still have the problem
Bimetal switch, condenser fan, overload sensor, start relay, timer switch, and lastly the thermostat freezer side
All ohms for compressor are normal range.
I have the last part today which is the run capacitor.
It is really funny that it is exactly the same as your troubles. Have you had the tech is for repairs? If so what was the trouble??
Thank you in advance