The normal equations for stability factor are:-
The second equation, which is normally in radians per meter, is applicable only at the muzzle, which is usually the point of minimum SG. Further down range, SG becomes a function of spin rate divided by velocity (both squared). All the other terms, except Cma, remain constant for an airgun pellet trajectory.
Of course, if you live somewhere where the air density is significantly lower than the ICAO value, then to maintain the desired SG will require reducing the spin rate by the appropriate amount. I have not yet looked at the implications of significantly reduced air density to see if the optimum SG values change. Living in the UK, it is not of large significance to us, even if we are shooting from the top of our highest mountains.

As for range being used as the primary variable, while shooters know the range they are shooting at, they do not generally know the velocity at any point in the trajectory. In addition, the study tended to suggest that the velocity did not in itself affect the optimum values of SG, as shown by the two velocities modelled giving much the same optimum values for given ranges. Remember, it is the ratio between the spin rate and the velocity which largely determines SG, and they are fixed at the start by the barrel twist rate.
The use of the average SG over the trajectory is also something of convenience, as it is relatively easy to find from the detailed trajectory output data, which includes SG values calculated for each time interval in the output. It is easier than trying to decide what the most relevant speed is and then using the appropriate SG value, and, based on the plots shown in the OP, seems to be relatively constant for both muzzle velocities and for both pellet designs. I believe it is therefore valid to use the average SG over the relevant range to produce the optimum.
However, as I have said before, there are still a lot of question marks about the work, which really is only in its infancy.