Official Luthiers Forum!

RH drop with a/c is a function of run time (coil area is fixed, and only so much water can be pulled out per minute of run time)...which is why folks that replace their older , smaller A/C units with over-sized ones often end up with less run time (and lower electric bills), but much less RH drop and ultimately less comfortable rooms. HVAC folks have formulas to size the unit to the space, and one of the concerns is getting enough run time to avoid turning a hot, humid house into a cool, humid house.

The short answer is that your window unit is not running long enough to drop RH, so either turn it down (if there is choice of fan speed/cooling settings which result in longer run time) or add a dehumidifier in the room to handle the job.

Those little combo heater/A/C units drop RH in the summer because water vapor in the room air condenses on the cool surface of the inside unit coils and drains that condensate to the outside. In heating mode, the inside coils or heating elements are warm (they stay well above the dew point of the room air), so while the temp may go up in the room, no water vapor is being added to the room air, so RH will drop. The only way to increase RH in heating mode is an add-on humidifier (with a water supply) or a separate free standing humidifier unit.