OK let me try to answer all your questions. I have 123 volts to the control board.
I have changed the heating element. I wired it direct for 24 hours bypassing the control board and using a probe thermometer with one probe in the freezer and one in the refrigerator. The receiver for the probes is outside the refrigerator. After 24 hours the temp in the freezer was 0 and the fridge was 48 degrees. I'm in south Texas so the temps are high and throughout this have peaked over 100 but the RV is in a covered storage with no direct sun and plenty of ventilation. The whole unit works perfectly on LP and responds well to temp controls on fridge. The heating element ohms out at 43.5.
I'll try the glass of water trick with the probe in the fridge. I have also tried boosting ventilation with a fan blowing directly into the back of the cooling unit. There was no change.