After looking at your picts once again, here's what i would advise you do:
Currently your fresh air is pulled through your hps, then into that vacuum (the vacuum alone creates a slightly warm exhaust btw (air is run over the electric motor to cool it), then dumps into the room.
Try this, kill the reducer on your Vortex output (go back to 4" or whatever its supposed to be), connect the Vortex to your HPS, connect your carbon filter to the other end of your HPS. This way the hot HPS air and room air goes straight out. Next, either use the suction power of your vortex to pull fresh air in (only if your room is air tight), or get a small 5" 120v electric fan to pump fresh air into the room.
Is the intake air coming from outside or from inside your home?
Mine comes from inside my bedroom, so the fresh air is already warmed up. The warmer the air you bring into your grow room, the more air you will have to cycle through. It can be 85 degrees in my bedroom and i can still maintain 90 under my HPS (summertime). I'm just pulling a lot of air through my rooms per minute (co2 is not an option for me).
I'd seal my grow room off so you can take control of the intake CFM's (cubic feet per minute of air). Next, maximize your exhaust output and fresh air input until you can maintain an acceptable room temp. I use a "cooling" thermostat, connected to my Vortex, which turns it on once the room temp climbs. It will go on every few minutes in the winter and stay on all day during the summer. Ace Hardware has a great, $12 cooling thermostat.
The smaller the room, the more wild the temp fluctuations will be. I attached picts of my small rooms. They work just fine now. I can run a perpetual grow of 17 plants (SOG). On extreme hot days i put a portable AC near the fresh air intake to control the temps....
hope this helps...
Oops, i just re-read your original post. We don't have the same Vortex fans,mine are 4"rs, if you can keep your output @ 6" then your fan should do the trick, just need to fine tune your set-up as per the advice you're getting on this board. Cheers.