I'm not really sure how effective compartment 2 is going to be in neutralizing the air. I had something different in my head. That deal needs to be air tight.
I can't tell if I am looking at this correctly, but I think I have some design tips that can help with your temps. You may be doing some of this, but I can't really tell from the pics.
1) Your intake appears to be high blowing right on the lights. You want the intake low as possible to draw in cool air and the exhaust as high as possible to get the hot air out. Hot air rises, right? You need a little squirrel cage fan inside the box to blow on the lights to dissipate the heat and increase air circulation. But you don't want your intake air being heated up right away. The light trap will cut down your intake power especially with a PC fan. Are you sure you need it if you are in a closet? I like my holes in the back for 2 reasons..1) you can't see them, it's more stealth 2) light really won't get to them if you have a wall behind it.
2) It looks like you only have 1 exhaust fan. For 8 CFLs, I would do 3 if you are using PC fans. You need more exhaust than intake to create negative pressure. This will help with smell leaking out of the box anyway.
3) I'm still concerned about height being issue. Your plants are going to stretch in the first few weeks of 12/12 and probably at least double in height. LST or SCROG will most likely need to be employed.
4) Timers. You need a heavy duty dual outlet timer, probably with a grounded plug. The best ones are digital with a battery back up. You can get a mechanical one, but if your electric goes out your cycle will not stay on track. Also, if you have fat thumbs like me and accidentally press down a button, your cycle will get a jolt. Not that big a deal in veg, but if you do it in flower you are increasing your chance of hermies.