The humidity where I live is just about always above 60%. Really guys, you acclimatise. The more you use air the more you feel it. In summer we can get nights that don't go below 74, and then I too find it hard to sleep, but 65 overnight is sweet. BTW my house is not full of mould or any other noticeable hazard due to not being de-humdified. House is >50 yrs old and made of wood, No rot I swear.
Each house has its own quirks. My last house heated and cooled differently to this one and it was about 1km up the road, so a little experimentation is needed.
Generally since heat moves to cool, I open up the house as soon as it is cooler outside than inside and leave it that way until it starts warming up outside. I close up the house and blinds etc a bit before the outside temp = inside temp. I leave it all closed until its cooler outside than in, then open up.
My last house had a large skylight that could be opened right up in the high point of the roof in a mezzanine study upstairs. Opening this was great, the hot air inside gushed upwards and out, drawing in cooler air downstairs. This is a good strategy to consider. In a 2 storey house opening the top floor windows also has the same effect to some extent.
My current house is 2 storey and there is a big temp difference between top and bottom floors ie in summer spend more time downstairs and in winter spend more time upstairs.
I recently retrofitted ducted air con and it has a fan setting and a dry setting and is zoned. The fan setting can be used to shift air from one part of the house to another to equalise temps eg in summer I can send the cool air downstairs to the upstairs. This costs much less than cooling and also introduces movement of the air which is cooling. In winter I use our wood fire, which is down one end of the house, and if needed move the hot air in that room around the house to rooms we are using. (the rest are closed off).
If the humidity really is way too high I use the dry setting (I'm guessing but >80-90%).
I only turn the cooling part on in the afternoon/evenings once we are home if the temp has been/is >85F and turn it off when I go to bed but will run it overnight if it looks like the temp is not going down below 74. Once you turn the aircon on, you have to close up the house and loose the free passive cooling.
Don't set an automatic turn on, turn it on manually, you'll save. Does you house really have to be precooled before you get home? It will only take an hour or two to cool down. You can stand a little sauna just for a short time.