An oversized AC is going to run more if you have your windows open when it's hot out although with humidity may actually work better as it'll run long enough to pull out some moisture (latent cooling).
If the issue is around fresh air your average pre-2000 house breathes plenty with closed windows and newer homes tend to have active ventilation (e.g. energy recovery ventilators).
I feel like I must be missing something or you live in a warm-temperate climate such that a heat pump heats faster than it cools (heat pumps go way down in heating efficiency as it gets cold out and most work very poorly when it's much below 0°F).