Most fans are designed to pull air and should be installed close to the exhaust. You have a couple things working against you: 1- even thought the fan is moving air, probably quite well, it is causing a restriction right at the beginning of your air ducting, reducing overall flow. 2- the fan has to work harder to push that air, putting more load on the motor, causing it to run warmer and introducing heat before you even get to the lights. Also, how are your lights arranged - all in line, 2 x 2, 3x1,etc and how are they ducted - all in a line, 2 inline then "Y" to one, all individually ducted to a plenum,etc? How big is the room? With 4 - 1000's You'll probably still need A/C, unless it's a huge room.
I just had an idea reading this, would it be possible to use a portable A/C to cool just the hoods? Have the A/C intake suck from the hot side and push cold air back in. Using something like this>
You'd have to make a plenum over the A/c outlet to duct to the lights, not a big deal. IDK if it's possible or if there is an advantage..maybe a smaller A/C unit would be needed since you are no longer cooling the whole room, just eliminating the heat at the source? I could see one down side being the constantly recirculating air would pretty much keep it running 24/7, or possibly cause short cycling of the A/C. I did a quick googling but didn't see anything.
There's also the option of water cooling your lights if you don't want A/C..again not sure of the pros/cons.
hope it helps