I don't know how many motors each flap section has.
Sure you do. I just told you. Two motors; one for in board flaps, one for outboard flaps.
Also although they work hard in the air, with the gear down, cooling is much better.
Why does putting the gear down cool electric flap motors? Further, for a given airspeed, how does the gear have any effect on the load under which the flap motors are operating?
The answer is the same in both cases...no effect.
They'd also not work very hard retracting.
Not so. The load on the torque tubes exists up or down.
Don't you think it would work?
I don't speculate. Has it ever been done before?