How does the outdoor temperature and humidity compare to what it was when you were getting 48 to 51% relative humidity in your home?
If it is considerably cooler outside the run time of your heat pump would be much less and it could be running short cycles which does not provide enough run time to do any amount of dehumidification.
You need a thermostat that will allow for a wider temperature differential spread, like a SWING adjustable thermostat. This will provide longer run time cycles and might help improve dehumidification.
Your home should be checked for its infiltration rate which should be reduced to .4 air changes per hour. In other words your home should be as well weatherized as is possible.
The duct system should be checked for any air leaks coming into the return or any air leaks in the supply duct system. Additionally, the install may not have been done with the proper best practices sequence procedures and therefore the system may not be operating at its peak performance level.
The blower should be operated on the cubic foot per minute rate of 350 CFM per ton of cooling. The heat pumps may be oversized for the actual heat-load conditions!
There is a high possibilty that this home is not get enough fresh air ventilation during calm winds and moderate temperatures.
Consider that amount of natural infiltration varies with the velocity of wind and the temperature difference outside verses inside. During most of the non winter, the natural venitlating is much lower than .4 ach and more like .05-.1 during calm winds.
With a 2,500 sqft. home with .4 ach is 130 cfm of fresh air with an outdoor dew point of 70^F, to maintain 75^F, 50%, 55^F dew point, you need to remove 3-4 lbs. of moisture per hour. How wide of dead band thermastat will you need? It is impossible with a small cooling load for any a/c to provide <50%RH during these conditions.
I suggest that supplemental dehumidificationis the only reasonable way of get to <50%RH during low/no cooling loads that the poster is describing.
Also, I suggest that .2 ach is adequate for fresh air during mild weather to purge indoor pollutants and renew oxygen. Also consider that occupants add moisture to the space in addition to the moisture in the fresh air. Any cool wet weather with dew points +60^F require 1-2 lbs. per hour dehumidification to maintain <50%RH.
Unoccupied homes getting adequate fresh air change with have indoor dew points that similar to outside dew points when unoccupied. Occupants will raise the indoor dew point during all seasons. An occupant humidifyies the indoor about .5 lbs. per hour. Chances are that you need a humidifier during cold weather and a dehumidifier during moderate weather and adequate air change.
We would do better in getting posters to think in dew points compare to %RH.
I also think that a/c coil temps (evaporaters) are better measures of removing moisture from homes. If you want <50%RH at 75^F, you need a <45-50^F coiling coil temp. Measuring air flow is difficult even in lab conditions.
Short cycling a/cs do not remove significant moisture.
A whole dehu maintains <50%RH without any cooling.
I do agree with much of your post, but leave view that one should expect <50%RH with adequate fresh air, low/no cooling load and normal occupancy.
Regards TB