Very nice troubleshooting based on the block diagram. I would say that if it seems to ice up sooner than expected that the Freon is getting lower as this is a visual symptom to “Low on gas”. I would also say that the fan kicks off due to the low temperature due to the icing and the heat exchanger does not need cooling off by the fan. I also would guess that your relay is stuck closed but a good smack on the head should rattle its brain to let loose and shut down as expected for additional troubleshooting, give it a good rap.
Icing due to low gas or very high humidity and also give it a good cleaning as dust will help condense water that will not drain off like normal, the dust will attract the water and it will freeze due to low fan air flow being blocked by the dust again. Then due to your constant compressor running will cause the temp to drop as well.
So we will assume the overtemp switch is working as the compressor is shutting down when overheating, this will override the stuck power relay.