I've got to het to my ladies. I the space you have this is what I'd do.
=> filter (optional)= ===>cooltube =>fan==exhaust
That will work for cooling your light and air exchange
Air cooled hood, better yet in the space a cool tube.
4" carbon filter, if smell is a concern
4" inline fan (I run variarc transformers((speed controls)) on all my fans)
Partition grow area to around 42" give or take
Passive intake from unused portion of cabinet
Exhaust into over head cabinet if available
Box fan facing wall for air circulation, or tower fan.
I'll sketch it up later if you'd like, I have 4 very mature ladies to tend too
and 8 smaller girls
!!
Edit: btw looks like you're headed in the right direction. Did you start the seeds in 5 gal buckets? Probably better to "pot up".