use a separate inline fan to blow cold air through the ducting creating positive pressure in the ducting / lighting system, you can use the coolest air in the room or outside air to blow through the ducting
use a separate inline fan to extract hot air from the environment creating negative pressure in the grow space this can be mounted just above the lights ,
the two fan system will work well you can connect the air conditioner to the light system to push cold air through the light/ducting also to help cool the lights before they can warm the air of the environment too much
always try to cool down the lights directly or concentrate on cooling the lights not the grow space
sucking out warm air from the space and only relying on that 1 fan system is a losing battle when you have a room full of lights
as you are sucking warm air through the lights this does not help to cool them down very much
have you used a 12 inch inline fan before ?
peace