The real problem with these range hood fans is there isn’t enough room (height) to do much in, plus the static pressure loss because the air has to turn 90 degrees as it slings off the blade tips. And they used a 4 bladed fan (never use a 4 bladed fan when it’s installed in a square box).
A forward curved squirrel cage fan would work awesomely as it would be quieter except for 2 caveats - it needs a scroll around it to operate efficiently, and the motor would have to be in the inlet where it would be exposed to the grease particles that the filter would allow to slip through (kind of a no-no when it comes to vent hood exhausting).
A radial bladed fan could be used, and doesn’t need a scroll, but the motor is still in the air stream and radial blade blower wheels are noisier. Plus you would have to get one that doesn’t have 4 blades, and an inlet Venturi is really needed for a radial.
I looked at fitting a tangential fan into ours. The beauty of a tangential fan is it turns the air 90 degrees already, and the motor is somewhat out of the air stream. The static capability of a tangential fan isn’t real high so didn’t get far enough down the road with the design to try to implement and determine results. That might be a winter project for me.
Not the answer you were looking for I’m sure. These MoHo vent hoods were a bad design from the start - and the bad design has not evolved beyond the original design since.
Same goes for the bathroom fart fans.