The appropriate media quantity for a 9X48 backwashing carbon tank is 1ft3 of 12 X 40 mesh carbon. In addition, 10 lbs of 1/8" X 1/16" bedding gravel will be required.
While these amounts will fill the tank height to 2/3, the remaining 1/3 'Freeboard' space above the media, provides the appropriate amount of space needed to permit the media to lift, expand and recirculate (reclassify) during each backwash cycle.
Although some will fill the tank to the top with the maximum quantity of media, then will utilize a non backwashing In/Out head in a counter flow configuration (service flow from bottom to top), filtration tends to be less effective. Backwashing will eliminate both any solid iron debris that enters with the water from your retention tank, and reclassification of the media will eliminate any channelling that will occur over time through the media bed as water will always follow the path of least resistance.
While GAC has a great ability to rapidly remove chlorine and many other chemical contaminants, Catalytic Carbon offers increased efficiency and ability for removing some difficult to remove compounds such as Hydrogen Sulfide ((H2S) which causes rotten egg odor), chloramine, disinfection by-products (THMs, HAAs), and other challenging organic compounds. Catalytic carbon starts off as GAC which is then further heat treated to enhance its catalytic action without negatively impacting the adsorption capability which is the predominant removal method for regular GAC.
As carbon is most effective when the flow rate is less than 3 GPM per ft3, any amount of carbon is better than none. The usual recommended minimum quantity of carbon for a point of entry applications is 1.5 ft3 (10X54 tank size), but larger quantities will further increase both the water contact time with the carbon, and will also support higher flow rates with less reduction in filtration effectiveness.
The recommended backwash rate for carbon is 8-12 GPM per ft2 of cross section, so for a 9" diameter tank, this equals a backwash rate (= drain flow rate) of 3.5 to 5.3 GPM, with the higher rate being optimal whenever possible. Your carbon tank is currently setup with a 5 GPM drain rate.
If considering moving up to 1.5 ft3 carbon in a 10" tank, the drain rate will be 4.3 - 6.5 GPM, so replacing the current 5 gpm Drain Line Flow Control restrictor button with a 6.0-6.5 GPM version would be best. Since the Fleck 5600 is limited to a 7 GPM drain rate, the recommended maxim<m carbon tank diameter will be 10", so any larger quantity of carbon (larger tank diameter) will require an alternate control valve.