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Relatively new double pane insulated windows and only 2 are in sunlight, the rest are shaded. Three large gable vents as well as ridge vents.
There could stand to be more insulation between the top floor and attic, but it's not too bad.
The heat is from the attic mostly, which is extremely hot because the entire (black shingle) roof is in full sun all afternoon until sunset.
It seems to me that recirculating the air (say 80deg air from upstairs) is more efficient than drawing in fresh 100+ degree air from outside.
I've considered a small diameter ceiling fan in the stairwell above the return vent, it would be the easiest option and I believe it would help greatly.
But a ceiling fan won't exchange the air from the coldest room to the hottest like a ducted whole house fan would.
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It is very difficult to know what to recommend, what would work and what would not without seeing the situation(s). We don't know your duct work, you noise tolerance, the size of the space, ...
All we know is you are dealing with stratified air. You need to mix it up (the air, that is).
Get the cold air and pump it upstairs. Let it sink back down on its own.
Alternatively, get the hot air and pump it downstairs. Let it rise back up on its own.
Mix the hot air upstairs with cold air down stairs using a pressure differential (fan or fans). I've designed and built refrigerated and heated enclosures. It can be made to work either way because your house is a closed system.
Another way to do it is to close off the upstairs from the downstairs (think, a closed door). This makes two separate zone that won't stratefy as easily.
Honestly, your posts read like you already know what you want. If so, just do it!