This is just my personal opinion of how to make this work if you are in that much need for temp control.
I would separate the air conditioner from the vented hood and the passive intake. Then I would leave the intake completely passive. Then take the filter and put it on the open end of the light with the exaust from the light goint to the exaust fan going out.
Then I would take the intake hose for the AC and route it up to the top of the space, and the cooled out going air to the floor.
The you would use 2 timers, one for the blower and one for the AC(turn the AC to maximum thermostat setting with the blower on low). The timers would be set so that the blower and AC run at opposite times of each other. The blower turns off and the AC turns on and runs for 15min then cuts off for 30min, while the blower comes on for 30min and cuts off when the AC cuts on, cuts on for 15min, off for 30min, and the cycle repeats until night time when the lights turn off you can have the blower continue to run without the AC turning on.
This might take a little adjusting of the timing cycles to get it to work without wasting much energy and still keep the room at a livable temp during the hottest months.