The BLFC flow restrictor, controls the flow rate of water to enter the brine tank.
The injector controls the flow rate for the brine to exit the brine tank, and also controls the flow rate for Slow Rinse which continues to occur after the brine has been transferred from the brine tank to the media tank.
The Brine Draw cycle is actually 2-cycles combined using 1 setting, typically 60-minutes. Brine will be usually transferred from the brine tank within the 1st 15-minutes, and Slow Rinse will occur during the remaining 45+ minutes after the brine tank's air check valve is closed to prevent air from being drawn into the resin tank. The Slow Rinse cycle requires sufficient time to push the brine through the remaining resin while also rinsing away calcium, magnesium, iron, chloride and excess sodium to drain.
Some efficiency maybe gained by using a smaller injector such as your #1, but a smaller injector results in a longer Regen cycle, which is OK when there is sufficient time for the regeneration cycle to be completed before soft water is required.
If equipped with a 0.25 gpm BLFC, that is perfectly OK since the BLFC rate must be less that the injector flow rate. The Brine Fill setting will determine the length of time water will enter the brine tank, so with a 0.25 gpm BLFC, each 1-minute of BF will cause 0.25 gallons of water to enter the brine tank. Because each gallon will dissolve 3-lbs salt, each 1-minute BF change will cause the salt amount to be altered by 0.75 lbs.
Tank size is 12x48, 2cuft. with 5600sxt.
I suspect you obtained your softener from an on-line seller.
The usual tank size for 2 ft3 resin + gravel under bedding is 12" X 52". Since the price of softeners purchased online include shipping, online sellers will often not include heavy gravel under bedding, even as gravel is highly recommended, and so will also often reduce the tank size to further reduce their cost.
The 6 lb salt (total) setting does not appear correct. Salt settings are often stated as lbs per ft3 of resin, so a 6 lb/ft3 setting will consume 12 lbs salt (4 gallons water to enter brine tank) each regeneration cycle, which is sufficient to regenerate 42,000 grains of useable capacity in 2 ft3 resin.
An 8 lb/ft3 salt setting is the usual recommendation as that will regenerate 48,000grains capacity in 2ft3 resin, with higher quality soft water with only 6ppm hardness compared to 10 ppm hardness leakage to eventually occur while using a 6 lb/ft3 setting. FYI, 1 gpg = 17.1 ppm. Although a salt setting less than 6 lbs/ft3 will result in further salt efficiency gains, less than 6 lbs/ft3 is not usually recommended for a single softener due to increased hardness leakage resulting in lower soft water quality.
Compare the 2ft3 row in the chart below for capacity, efficiency and hardness leakage data for each salt setting column.