Well, it was a noble effort (if I do say so myself), but I ended up putting my window A/C in the attic today. This morning we awoke to indoor temp of 69 (yay!) and relative humidity 74% (not yay!). At humidity levels this high, hard-surfaced floors feel sticky to walk on, and carpet feels...crunchy? I went outside for a bit and started sweating. After coming back inside, the sweat did not evaporate, and in fact I kept on sweating. More concerning, RH above about 60% is not so great for allergy sufferers, and we have a few of those in the house.
My basement dehumidifier has been chugging nonstop trying to keep the RH around ~50. I put another dehumidifier on the 1st floor, and after running all day the temp/RH is 76/66 -- actually a higher dew point than this morning, probably because we all keep breathing. I could open all the windows in the house and let the outdoor air, with slightly lower dew point, dry out the house somewhat. But I know from experience that it takes many hours to do so, and it means our indoor temperatures would get too hot to sleep well tonight (it's in the low 90's outside right now).
So my new goal is to run the window A/C('s -- I'll probably put in 1 or 2 more on the 2nd and 1st floors, as needed) only until the RH drops below 60.