Well stated!Keep in mind that "Ba" and "Burn Rate" are over simplifications for a basic model.
If you do a caloric bomb test, you are placing the material in a vessel and igniting it while you measure temperature and pressure against time. When we do standardized testing, we get "standardized" results. I placed quote marks around that because when you then take those propellants and put them in cartridges of different sizes, with bullets of different diameters and resistance, you may get a different answer for the same powder just due to context.
Unless you are directly trying to calculate a moon shot where you cannot test or "take sighters", don't worry about it too much... YMMV