All any of us can go by is what you tell us.
This morning in post #5, you said both the softener and carbon filter were in-service but there now is no soft water even as there was soft water previously. You then detailed the current program settings for the softener which I commented on, in particular the 'C' setting.
Are you now saying the filter and softener tanks were swapped so the carbon media was being regenerated with salt brine? If so, I then anticipate the softener resin has not been regenerated but has been only backwashed. Since the carbon backwash rate will be higher than needed for softener resin, backwashing with the head for the carbon will cause the resin to be back washed too aggressively which may have resulted in the loss of some of the resin to drain, particularly if no upper screen is installed in the resin tank.
Although the heads may have been installed on the incorrect tanks, as soft water was present earlier on but is not now, it appears the resin's softening capacity has been totally depleted. When resin has been exhausted, it is advisable to regenerate with the maximum salt amount to restore the total capacity before regular ongoing use.
Even with installing the correct control valve for the softener media, the 'C' setting programmed at 48 is incorrect for 1.5 ft3 of softener resin.
Follow down the Resin Volume column at the left of the linked chart until you reach 1.5 ft3. Scanning across right will show various usable capacities that will be regenerated when using the specific amount of salt shown at the top of each column. As the salt amounts are shown in pounds per cubic foot of resin, then for your 1.5 ft3 softener, 8 lb/ft3 will be 12 lbs salt to regenerate 36,000 grains capacity.
The BLFC will control the fill rate to the brine tank. The BF setting is the number of minutes water is to enter the brine tank. As mentioned, each 1 gallon will dissolve 3 lbs salt. You confirmed your BLFC flow rate is 0.5 gpm, so 0.5 X 8 minutes BF = 4 gallons X 3 lbs/gal = 12 lbs salt to be dissolved each regeneration cycle.
At the bottom of each salt setting column is an indication of Hardness Reduction Efficiency which is often referred to as salt efficiency in grains per lb of salt Also indicated is a hardness leakage factor which is directly related to water quality for each salt amount.
Water treatment usually involves compromise. A higher efficiency setting will reduce salt consumption, but water quality will also decline and regeneration will be more frequent due to the lower amount of capacity to be used between regenerations. An 8 lb/ft3 setting is most recommended as it will usually provide the best balance of salt efficiency, capacity and water quality.