How does the A/C struggle? Does it run all the time? Cycle often?
Ideally, you want your A/C to cycle about twice per hour. You want it to run a long time, as that is when it starts removing humidity. If it cycles too often, the evaporator just gets cold enough to eliminate humidity when it shuts off... Which takes between 5-10min if I recall to reach the point in which it will take humidity out of the air.
Just playing around with my thermostat "swing" setting, I can see a change in humidity levels. If you set at 72 with a 1/4 degree swing, it will turn on at 72.25 degree and shut off at 71.75 degree. With that setting, my house was mid 50's relative humidity. Increase it to ½ degree swing (on 72.5, off 71.5) I was around 48-50%. I found the sweet spot at .75 degree swing, in which my RH levels are around 45-48%. The house feels even cooler now with more humidity out.
We have window people coming today to plan on replacing our upstairs windows which are completely shot, so that should help big time. Upstairs, you can feel the higher humidity due to leaky windows. We already had our lower level windows/doors replaced and that was a big help.
I also run a dehumidifier in the basement during summer, which drains right into the drain, so I never have to empty it. Helps keep the basement around 45% RH.