Hello,
The 'Big whole house fan' is a very interesting subject to me. This is just an opinion.
I am no expert on this, but from my limited experiments with DC motors as fans, I think I would go with a BIG DC (over 100vdc rated) permanent magnet motor with VERY big ceramic magnets in it. Lose the belt drive and go with direct drive to get more for less power. My theory is the bigger the ceramic magnets (the field) inside the motor, the more 'fan' you will get for less power.
For what you are talking about I would get something much bigger than just a treadmill motor.
You may have to weld up a new steel mount for the big motor since it would weigh so much.
Your fan blades are large at almost 4' in diameter, so my wild guess is you may want it to go 400-600rpm??
So for a 12v system like yours, a would first try a big motor with ratings around 130vdc/ 4000rpm / 10-15A . I have never tried anything that big though. Sounds like fun though!
Hooked to 12v batts or direct 12v solar panel , it might only use around 60-100watts of power to run and put out quite a lot of wind. But I am quessing somewhat, it is difficult to know for sure.
It is difficult to estimate how much CMF you really need and thus how much watts that will need to be used in a complex application like yours.
If you could somehow have a relay that would hook the fan DIRECTLY to one of the solar panels, you could get even more for less power by skipping the batteries when the sun is out. I have hooked my 31 inch floor fan directly to my 45Watt (actually 25W output) HF solar panel, and it really runs like a jet.
You probably won't get the kind of CFM you mentioned, but it should be quite good I suspect especially if the fan has nothing resisting the air flow into the attic.
-Hopefully others can share some more experiences. -Hope it works good.
