Run the air and don't open the windows at night. Should get you down to 30% around here, or even lower. Humidity is the most high at night. We have to run a humidifier if we run the air or things get staticy. I would only air the house out when co2 gets above 700, but you can time this so that you pick the days to let in fresh air.
If you open the windows in the summer, then do it when the humidity is super low in the afternoon, and on low humidity days. The warmer air sucks, but it is easier to cool air than to dry it out.
We had dehumidifier in Missouri and it was an energy hog and stuff. It also put out a lot of heat, which you know.
I would avoid it at all costs by planning your days better and/or keeping the house closed up if you can.
It looks like we turned a corner. The 10 day forcast looks a lot better than what we just went through. Lows in the 50s this time of year means dry air, usually.