I would say the 4' x 4' x 2' is possible. From the top of my cooltube (400w hps) to the bottom of my pots (15L) is 41", but I used LST and Scrog to control the height of the plants. You could also look into super cropping, topping, fimming, all kinds of methods to keep your plants short and even higher yields.

My temps are also a little higher than optimal, but still within range... You really need a good fan, and by good I mean it should be able to handle enough heat from the light in the cooltube so you can pull the air out with the fan, instead of pushing it through the cooltube. Then you can hook up your carbon filter to the other side of the cooltube. The second link in my sig goes through all the ways I've been trying to get things to run smoothly, and I finally got it how I want it.