Your 45,000 grain softener will likely contain 1.5 ft3 of resin. For that size softener, the Capacity setting between regeneration cycles will be typically programmed to 36,000 grains which will utilize an efficient 12 lbs salt per cycle. To dissolve 12 lbs salt will require 4 gallons water to enter the brine tank each cycle.
Does placing 4 gallons water into the brine tank while filled with salt cause the fluid to overflow out of the tank overflow fitting (if equipped) or cause the safety float to be lifted? If so, the Capacity setting could be reduced to 31,000 grains which will need only 9 lbs salt, lowering the Brine Fill requirement to 3 gallons.
An alternate method to allow a higher Capacity setting with a small brine tank is to equip the brine tank with a salt grid. This is a perforated platform that raises the salt above the bottom of the tank, permiting a substantial portion of the water to remain below the salt where it will not be displaced by salt. With less displacement, the fluid height will remain lower and so less likely to overflow or lift the safety float.
Edit:. As per the chart linked above, an 11" square brine tank is shown suitable for a softener containing only 1 ft3 resin while using an 8 lb salt setting. Adding a salt grid will increase the suitability to 1.5 ft3 resin, but only while using maximum 9 lbs (6 lbs/ft3) salt per cycle.
