Hmmm, I just checked, my BD time is 60 minutes in on both my katalox light tanks and my softener resin tank.
These are different uses. In the softener, you draw gallons of brine, until the air check valve shuts down the draw of brine. Then the BD time continues, and you still pass water through the injector through the resin. That added time is called the slow rinse.
In a typical design, the injector is chosen to exhaust the brine in about 15 minutes, and the remainder of the 60 minutes is slow rinse. But not exactly. The amount of brine to draw will vary, even for the same amount of resin, according to how much salt you plan to use. There can be a fairly wide range from even less than 4 lbs per cubic ft of resin to over double that. Normally the BD time is a time that will be reasonable for a range of draws. Not that it could not be customized for each draw time, but for simplicity it is usually not.
But whether you draw for 10 minutes or 19 minutes before the brine has been sucked in, the BD might be still set for 60 minutes. If the brine takes 20 minutes to 29 minutes, the BD would be increase to 90 minutes. I enjoy some complexity, so I might pick other BD times.
For a filter sucking pot perm solution in your case (I presume), or a bleach solution in my case, the regeneration does not suck the solution down all of the way. My BD for the filter is only 4 minutes and my BF is zero. In my case, I regen every 3 days. On the 11th regen, the 15 gallon solution tank has been sucked empty. Every 33 days I add a gallon of bleach, and top with water (soft water now that I added a handy spigot for that). If my filter had a BF=1, that could clear the line of bleach solution, but it would gradually dilute the solution.
My filter relies on RR to clear the chlorine from the media. I have not smelled residual chlorine from a faucet.
I also have #00 purple on my softener tank.
For your 1.25 of resin and if you ran 7 lb/cuft of salt, I estimate you would draw your brine in 19.8 minutes. That is right at the limit where BD=60 might be enough. Classically you would multiply your ~20 minutes by 4 and set BD=80. But that factor of 4x has some margin. So a factor of 3x is probably enough to avoid residual salt taste after each regeneration. If you use 8 lb/cuft, then you would want to bump up your BD time. You could step up to a nice safe 90. Or you could choose as little as 70. If you wanted to test to see if your BD is actually enough, watch for significantly elevated TDS in the first gallons the softener puts out after regen.
The softener remains in bypass during BD time.