I don't think that air flowing through the room too fast is the problem. On the contrary, if it is hanging around long enough to get heated up, it's more likely not moving fast enough.
A cost effective solution would be to have both fans at one end of the room exhausting air, and have a cooled passive intake at the other end. If both fans move about the same amount of air you would be doubling your airflow. Think about it, if each fan moved, say, 100 cubic feet of air per minute, then with one intake and one exhaust 100 cubic feet of air would move through the room every minute, but if both were moving 100cfm out of the room, and chilled air was free to enter the room, then that would go up to 200cfm.
Ventilation is about moving as much air as possible until you get to a manageable temperature. Forget this idea you have that if you put cool air into a room with a heat source, multiple in your case, that air will stay cool. The heat from the lights will be transferred to the air, and then you need to get that air out, and keep more cool air coming in.
The only time you can have too much ventilation is if the room is too cold, you are using co2 and it's all getting sucked out of the exhaust, or the humidity drops below acceptable levels.