I have worked at a facility that had BAF's. I also replaced several VFD on them (Mfg defect) not BAF issue. They are impressive, they are massive. The big ones have 3-5hp motors on them driving a reducer. An issue with a BAF is if there are lights above the blades, they make a shadowing strobe effect.
I just installed 4, Emerson HF1160 fans in our 2400 sq/ft 40x60x17 shop. They are 60", 3 composite blades and put out a little over 10,000 CFM on high. I had also used these on my porches when we built our house about 5 years ago.
They are mounted about 18' from the floor. Low speed would probably be good for pushing heated air down. On medium speed, they are quiet and can feel a light breeze. On highest speed, they will part your hair and blow loose objects around with noticeable blade sound, but not excessive. Controlling them Lutron Toggler fan controls. Available in black, white or brushed steel.
I have pictures on my build thread.
CT