Taping some of the more expensive allergen/mold rated 20" x 1-2" furnace filters up to a cheap box fan works pretty good for general scrubbing of a room. Check out DIY corsi-rosenthal boxes for more effeciency. Not really true hepa.. but test prove the cheap box fan filters scrub like 90% or more of the overall air particulates out of a room. Even better than the smaller single hepa type air purifiers, simply due to having like 30 times the filter surface area, and way more air flow. I make and use them all the time. Having a few of them running constantly outside the clean tent would keep the majority of dust off your stuff in the room, and help basically double filter your main flow hoods pre-filter, and keep the main filter extra clean & lasting for years. Save you the small fortune of buying extra hepa rated units to try and clean the whole room to lab standards.. That does sound nice though!
I think you could get away with just strapping an FFU to the side of the tent, and work with that as is. Instead of swirling the same air around inside, make it blow all the way through and exhuast out the other side, so it flows through in one direction through the whole tent with positive pressure....
As far as the inline carbon filters go, i'm pretty sure that eventually they build up and start releasing whatever crud right back into the air. At least in aquarium\water filtration setups that is the case, so not sure I would trust them not to shoot out PM spores or whatever back into the air around your cultures\grow space.. especially a used one that was around plants, etc..