Ok as promised I just knocked up a couple of bodge pics
Now let me explain that both these pics are views of the box as I'm pretty sure I'd make it & both views are from the front
However one is the back half of the box & the other is the front half. I'll explain each pic as I go along so hopefully you will grasp what I'm on about fairly easily.
Ok, this picture is of the back half of the box Remember you do have some depth to play with so I don't see much if any of this being a problem.
If you are silencing the outlet you're going to want to silence the inlet too So on the right in the back half of the box you have an air input & then the silencer. I think you said about using a 600W HPS though I could be mistaken, but assuming a 600W HPS I'd go for a 5" fan on the input. This fan won't be working against any real air pressure at all, so to keep it as quiet as possible I'd go for something like a 125mm S&P mixed flow fan. Following the fan is a 90 degree bend & then solid plastic ducting, both of these are readily available & cheap.
The bottom of the ducting I'd cut a small piece out of the duct facing the veg chamber & a larger piece out towards the flower chamber, the base of the duct wants to be hard up against the bottom of the box. I'd put a thin piece of plastic up inside the duct from the floor of the box to above the top of both of the removed pieces to separate the airflow, so looking at the duct from the bottom it'd look like a circle with a line across the middle.
Then I'd box in around the duct to the flower chamber side obviously leaving the vent to the veg side open & totally separating both chambers.
You now have forced air input to both
Here's the front half of the box.
The CF is in the front half because you'll never need to change the silencer, but you sure as hell will need to change the CF
The top of the flower chamber is open to the top portion where it hits the CF, then the fan & then the silencer & out the opposite side of the box.
The fun bit is the light baffles There is a gap between the baffle in the veg chamber & the very top of the veg chamber, now personally I'd make this adjustable with a sliding piece of say hardboard so you could adjust the airflow into the flower chamber. I hope it's pretty easy to see the idea. Air going in on the left hand side, down, around the 180 degree bend & out into the flower chamber.
Light will not go round corners unless it's reflected or it happens to pass close to a black hole I'd suggest a coating of matt black paint on the inside of the light baffles, but I doubt it'd be needed..
Any questions please fire away. Obviously I hope this helps