Unless you are attempting a 'sealed room', your 440 is a PERFECT exhaust fan; just run it through the hood, then the fan, then the filter, then out. Intake may be passive, and in your setup, holes cut in the FLOOR of the space to take advantage of the cooling thermal mass of the concrete beneath are PERFECT!!!!

I'd go with white Panda film instead of mylar, but everything looks good. That's why so few responses. You got it. Really!