So, you have 480 cf volume tent plus an air conditioner. I think you will be doing great (unless your in a 120f degree garage) and you could always add an intake fan if needed.

About pushing rather than pulling the hot air.... Like our friend Rusty said, pushing the hot air will allow hot air to leak through hood seems and hose connections if you have any leaks. Your hood seems to have only one duct so you can't really push it through anyway so it's a moot point. You don't have to put the fan right at the hood. Your preferred method (fan to duct, into tent, to hood) sounds good. Anyway, you could, and may want to make adjustments along the way. I'd figure on that.

There is a theory about the heat from the bulb will cause your fan to burn out, melt, explode, catch fire, insert disaster dujour here ___________. I say BULL! You have a 400W bulb, it'll be no problem. Even with a 1,000W bulb the duct barely gets luke warm to the touch. I think that theory is over thought and scary urban legend.