The salt setting will influence the 'slippery feeling' of the soft water whereas the hardness and capacity settings will affect the number of gallons delivered before regeneration will occur.
As 1 grain per gallon = 17.1 ppm hardness, soft water containing 15 ppm hardness, may not feel as slippery compared to soft water containing 6 ppm hardness, even as each will contain and test less than 1 gpg.
A specific softness level for residential usage is not usually critical as it often will be in a manufacturing or steam boiler feed application. In some home applications, 3 gpg or lower will be acceptable to the occupants, whereas in others, less than 1 gpg is expected.
The following link is to a chart which shows at the bottom, anticipated hardness leakage through a softener for various salt settings. Those leakage amounts will not occur immediately but will after numerous regeneration cycles. Lower leakage (higher water quality), will result in less salt efficiency as a higher amount of salt will be required for each regeneration cycle.
https://terrylove.com/forums/index.php?attachments/resin-chart-jpg.53316/
The amount of salt used is calculated by the BF setting (minutes) X BLFC flow rate (0.25 gpm) = amount of water to enter the brine tank. Each 1 gallon will dissolve 3 lbs salt. As Reach4 stated, your current 16 minute BF setting results in 8 lbs per ft3 or 12 lbs total salt for your 1.5 ft3 system. That salt setting is frequently recommended as it will regenerate 36,000 grains usable capacity in a 1.5 ft3 system, and provides a great balance of capacity, salt efficiency and water quality.
In your situation, if you haven't utilized a softener previously, I suspect any calcium and magnesium that has accumulated within the pipes and water heater over the years, is now being dissolved by the soft water, thereby adding a few ppm hardness back into the water which is affecting the 'feel', even as it remains less than 1 gpg. Expect that to continue until all mineral residue has been eliminated which could take a few months depending on how much accumulation there is.