If humidity is a serious problem you could consider getting a proper central unit installed. A lot of new construction in the Gulf Coast region is including these in the HVAC systems. It's like a mini 1/4 ton A/C system inside your system. I had one that came w/ the house but it didn't last very long (Honeywell). Replaced it with an Aprilaire unit.
I can tell when my dehumidifier is off or not working because I'll see really bad condensation forming around registers. Keeping RH below 55% is an extreme battle this time of year. My dehumidifier runs 24/7 for about 9 months of the year and the main heat pump runs about 80-85% of the day.