[goodellj]

I have two other suspicions that might be worth investigating. When your AC unit operates as a heat pump, it is still an AC with a compressor but is moving heat from outside to inside. If the unit is humming but not operating, maybe there is not enough electrical voltage for the compressor. This can harm your AC compressor and cause permanent damage, but you say the unit sometimes still operates normally.
2nd idea: My Montana has a Dometic thermostat with 2 zones: zone 1 has the propane furnace and the living room AC unit, and zone 2 has a bedroom AC unit. Operating the AC on zone 1 seems simple as long as I stick to heat mode for times when I want the furnace and cool mode for when I want the AC. But the auto mode gives strange results with the AC and furnace both operating at alternate times. For example, the furnace keeps us warm at night. While cooking breakfast, the AC might kick on. Open the door to go outside, the furnace runs. The sun comes out and the AC runs. The sun goes behind a cloud, the furnace kicks on. And so on. Because of this I only operate the thermostat on the heat or cool modes, and never the auto mode. Are your AC/heat pump and furnace all on one thermostat and zone? Maybe your issues are really due to a complicated or an inadequate thermostat. How does it work to have the thermostat call for heat and have 2 heating units (HP and furnace) available to respond?