Got it.
My media tank is 10x54 inches. It holds 1.5 cuft of Centaur Carbon. The media is said to last maybe 7 years or so. This is not GAC. I bought my system in November 2012. My tank uses 5 GPM backwash with a 10 that 10 inch tank.
Is your tank M 12x52 or what? That would correspond to 2 cubic ft of media. A 12 inch tank should use 1.44 times as much backwash as a 10 inch tank, which comes to 7.07 gallons to match up to my 5 gpm... but 7 is probably close enough.
For the programming of mine, BF=4 meaning that solution is drawn for 4 minutes. It is drawing at the rate of 0.3125 GPM.
My BF=0, so that it does not refill the water.
Your controller is a mechanical controller, so adjustments are going to be different. If you can, you will want to minimize brine fill (where water is added). That could let you refill your solution tank after several regenerations. If your unit continues as it is (without making adjustments) every 3 days (each regen) will want to add about 14 ounces of bleach. This is simply scaling from what I do. It is possible that you could come up with something that would save that frequent chore. Perhaps you could put a pool chlorinating tablets into the tank and let that do the job. Then you could go a long time between visits to the tank. I am not a pro.
I set my electronic calendar to remind me to refill every 5 weeks. Every third time, there is some left in the tank, but I still add my gallon of bleach, and top off with water. If you could top off with soft water, that would be better. I am actually using 121 ounces of 8.25 bleach instead of 128 ounces of 5.5% bleach, because that is how the bleach is sold. It is a little stronger than the original recommendation, but I think it is close enough.