Your original question is an interesting one. Heat is always trying to move in a direction that equalizes temperature. If the inside of your house is warmer than the outside, heat will naturally leak out. If the inside of your house is cooler than the outside, heat will naturally leak in. Opening windows or doors will accelerate this process. Meanwhile your air conditioner is actively pumping heat out. All my life I've been told that it's bad to open the windows/doors when the air conditioner is on, but I think that advice assumes that it's actually warmer outside than inside, such that opening the windows amplifies the natural heat transfer in, which works against what the AC is trying to do.
But if it's colder outside, that means the natural heat transfer is going outward, and opening the windows just helps the natural heat transfer go faster, so then maybe opening the windows while running the AC would result in faster cooling than doing either thing alone. Something feels very wrong about doing this, but the more I think about it the more it seems like a valid tactic if just opening the windows isn't good enough on its own.
The attic is a wild card. The sun beats down on the roof throughout the day, this energy is absorbed by the roof as heat into the attic, and so the attic gets really hot. The thermal mass of the attic is radiating heat in all directions throughout the night as a result. Seems like a fan in the attic to exchange the attic air with outside air would help minimize the differential in temperature between the attic and the outside. Insulation between the attic and the rest of your house would also help, as would putting light-colored material on the roof to absorb less of the sun's energy in the first place. But as you point out you're only spending some $200/year on the air conditioning, so there's only so much capital expense that makes sense here from a financial perspective. You'll improve comfort with improvements to the attic, but saving money is dubious.
Remember also curtains/blinds. These should be closed during the day as much as possible to minimize heat transfer into the house through the windows. We live in a milder climate than you, but our general playbook during summer in a house with no air conditioning (except in one bedroom) is this:
1) Open windows in the evening as outdoor temperature falls below indoor temperature, close windows in morning as outdoor temperature rises to match indoor temperature.
2) Run fans when the windows are open, to speed air exchange and thereby accelerate heat transfer.
3) Close curtains/blinds when the sun is up, especially on the direction of the house that is getting the most sun.
4) Minimize cooking on especially hot days.
Combine all this with air conditioning usage during the hottest part of the day and you should be on the right track.
