I think this quote from Davis sums things up nicely.
"The products of the burning of black powder have been studied by a number of investigators, particularly by Noble and Abel, who showed that the burning does not correspond to any simple chemical reaction between stoichiometrical proportions of the ingredients."
If you look at the analysis of the burning mixture in Davis, something sort of interesting is noticed. Of the solid products (55.91% of all combustion products), 8.74% is sulfur. This means approximately 50% of the sulfur in the formula is ultimately unutilized.
If anyone in charge here would like to check, I'd be happy to provide my collection of known IP addresses used by Anyka, Ushie, etc.
I agree this is a fair analysis, and that was my point that simple stoichiometry can't easily be used to define the reaction. Thank you for the suitable quote.