I have been playing around with QuickLOAD to see what I can find-out about this question. There seem to be two parts to it. First, is it possible to get 14.6 grains of AA #9 into a 357 Sig case under the Speer 125 grain GDHP? Second, if you can, what would the pressure be?
I used the current Speer and Hornady loading manuals for the 357 Sig 124 grain XTP and 125 grain GDHP data. In Xcell, I plotted all of the data for the powders that appeared in BOTH manuals, showing velocity vs charge weight. (Unfortunately, AA #9 is not in the Hornady manual for this bullet in this cartridge.) Generally, for a given powder, the two sets of data created lines with the same slope that were off-set a little bit left or right, probably due to different lots of the powder being used in the different labs.
For AA #7, the two data sets plot as nearly a single straight line. But, Speer data goes higher (as with all of the other powders, as well). However, if I use QuickLOAD default values, I get a line that is above the actual data line by quite a bit. If I adjust the case volume in QuickLOAD to 20.80 grains of water, the QuickLOAD velocity vs charge results match the actual data very well.
Now, if I use the same case volume for AA#9, I get a load density of 101.6% with 50,582 psi and 1544 fps. So, for a case that big, QuickLoad thinks the powder will come close to fitting, but still would need a "Ba" adjustment to get pressure and velocity to match the data.
So, there is still the question about getting the powder into the case. You wrote that the largest case capacity that you have measured is 19.7 grains of water. But, the 357 Sig case changes shape a lot when it is fired, with the shoulder moving forward substantially and the whole case getting shorter.
So, I need a little more info about your case volume measurements. First, what is the capacity after it is fired, before resizing, and what is the UNSIZED length of the case used to measure that capacity. Next, what is the capacity and length of the same case after it has been sized to fit your gun?
I do not have any experience with AA #9, but I do with other fine-grained ball powers, and I find that I can fit significantly more powder into a given volume if I tap the container to settle the powder. Bulk densities greater than 1 grain of powder per grain of water capacity have been achieved without putting physical pressure on the powder charge. So, with QuickLOAD giving a powder space of 14.545 grains of H2O under the Speer bullet (with the case capacity adjusted to 20.8 grains), getting 14.6 grains of AA #9 into the case may not be such an impossible task, IF the real capacity is anywhere near that value.