yes, definitely keep the 6" fan. the inline one, that is. i'd recommend for anyone reading the CAP ValuLine and green hydrofarm fans as inexpensive investments. the increase (300~ + cfm) to a 6" from a 4" is priceless. well, it's actuall ylike 20 bucks, but a priceless twenty bucks.
that duct booster fan you have (i have a few, and also a few 6" inline) wimply can't handle as much static pressure as a strong inline fan.
static pressure? that's when you have to pull through a carbon filter, fast enough to still exchange all the air in your space in 3-5 minutes. on top of that, i and many others, blow through soundproofed A/C boxes, through multiple hoods, and through an exhaust vent. roughly 30 feet of ducting/hoods on that run, and my 440cfm fan blows through all of it. strongly.
your ductbooster won't have the strength to pull through a filter, shoot through a hood, and out you rbox and do it fast enough. can't handle the pressure.
do a test, put 10 feet of 6" duct on that booster and one turn in the duct. like a curve in either direction. feel the barely discernable air movement out of it. do the same with the inline.
anyway, i belabor the point. you can never exchange your air fast enough, and when you have to pull through ducting and dense carbon packed filters, you'll need the strength.
.sd
hey, good luck!