Your home cannot be at a pressure that is different than the pressure outside without an attempt to equalize.
In practical terms, that means if you put an exhaust fan up near the ceiling the house will be under negative pressure-----you’re sucking air out of the house.
Nature doesn’t like that and it will want to equalize. So…underneath every crack, around every [leaky] window, and every time you open a door air will rush in to equalize with the outside.
You’re sucking air out, and an equal amount of air is coming into the home via the windows, doors, flues, walls etc. For example, if you put a 200 CFM exhaust fan near the ceiling (and it’s actually moving 200 CFM) than 200 CFM is entering your home vis these cracks. (and a “crack” may simply be opening a door)
In commercial buildings that’s called “make up air”; it’s air that’s “making up” the air lost due to exhaust.
The problem is that this make up air is outside, untreated air. Your A/C system is designed to recirculate 90% of the air it cools. If you add exhaust this make up air will have to be cooled.
If you add an exhaust fan and don’t take this additional “cooling load” into consideration your A/C system still won’t cool because you are now cooling part of the neighborhood.
If you do take this outside air into consideration you will quickly realize that a 3 ton system is no longer gonna do the job. You have a much higher cooling load due to the exhaust/make up air and you’ll spend potentially a lot more cooling your house and back yard.
IME, Rick’s (and others) approaches will do better. Contend with the envelope first; roof, roof insulation, windows, doors and walls.
Then deal with the HVAC. As to the heat upstairs, either adding a cold air return upstairs (to bring that heat back to the furnace to be treated) or adding a “mini-split” as GaryM mentioned will do better.
Exhaust fans are excellent to ventilate/exhaust attics. (And even then need make up air via ridge vents or soffit vents)
But IMO using exhaust fans to ventilate/exhaust the living space is a bad idea and will not work.