I like RJ's diagram except I would turn it horizontal... does that make sense? & reverse the air flow... here's what I mean...
You would have your Can Filter & Fan hooked up together in the middle where he has "Fan" designated. Rather than pulling it from the 6 lights, pushing it through them as you had originally outlined (more on that later). Then you would have 2 exit ports through your ceiling and/or walls. Make sense? I'm just looking at the diagram as if from the ceiling looking down.
Pushing vs pulling... if you push it is less effective in air movement, no doubt about it. However, by pulling air directly into the filter then through the fan & pushed out through the tubes takes advantage of positive air pressures. Essentially, every leak/connection/hood down range of the filter will have air escaping back into the room with a push system (some heat, oh well). If you pull w a fan at the end of the line, it will create negative air pressure within the tubes and your unscrubbed air will leak INTO the lines. If you push, all the air going out is scrubbed, if you pull, not so much. Hope that makes sense.
To compensate, you can tie in two 8" booster fans at both of the exit ports, should air flow not be enough. These will not create negative air pressure & suck odors in as the max fan will still be stronger in creating positive internal pressure. This is a little trick that works. Peace.
BTW, get a roll of shrink wrap from WMart or the local U-Haul... works great/better than anything else to seal the connections. Peace.