Are you saying I should run the duct from another room into the cool tubes and back out the grow room into the other room where it started
Yes, the ventilation for the lights should be its own separate circuit independent of the rooms ventilation/cooling . If you can pull from one area and dump it to another, that'd be better as you won't be recirculating the hot air.
I'd run 2 intakes, 1 exhaust. Something like:
8" intake>flex duct>8"cooltube>8"cooltube>flex duct>
......................................................................................... >8"×8"×10" "Y"duct>10"fan>outside
8" intake>flex duct>8"cooltube>8"cooltube>flex duct>
Then close up any room vents, except for the AC exhaust, and see how it does.
4 plants per light x 4 lights x 4ozs ea(min. I'd hope) = 4 lbs. That's what I'd be shooting for at the low end, although I'm usually around 6ozs per plant growing 4 per 600, so that'd be closer to 6lbs, if you can control the environment.