This is a suggestion and should be construed as that only... a suggestion.

The bigger the fan, the better. That would mean less time running to cleanse the air and you might be able to get away with 5 mins every hour or so...

Minimum 500 cu. ft./min.

If you are going to air cool your light, that would need to be on a second fan.

Think about the DIY carbon filter on this site.... it pulls the air through the filter, through the ducting, and then spits out clean air. There is NOTHING on the other side of the filter... it's capped off. That makes the filter pull the air through the activated carbon... thus cleaning the air. If you had a filter between your reflector/hood and exhaust fan, it would clean MINIMAL air.

My suggestion is this...
run 6" ducting from your air cooled hood and shoot it out of the cabinet... maybe into the wall. Remember that 90 degree bends in ducting increase the need of more airflow... the less bends, the better.

install your carbon filter with 4" ducting or so and also run it out of the cab.....
yes.... two exhaust ports.

that would be the most effective way to keep it cool and keep the smell down, IMHO.