My older house had an American Standard heat pump. The fan in the air handler had a 30 second delay on it. When the thermostat switched off, the AHU blower would continue running for 30 seconds or so to dry out the A-coil. In my new home, it has an older Rheem oil furnace (about 20 years old, coupled with an old kenmore air conditioner) The system does great on humidity, but the coil is developing a "dirty sock" odor. I was wondering is if the same sort of delay device can be installed on the furnace's fan unit so that when the heat pump shuts off, the AHU will run a little while longer and dry out the coil.
It takes close to 10 minutes for the air to dry off a coil. Turn the thermostat fan option to on and see if that solves your issue. That water going back into the air raises the humidity level in the house though,just a FYI. The 30-60 second blower off delays were to get a wee bit of free cooling since the coil was still cold from the cycle.