I think you've made a valid observation Miller. The pressure/distance curve:
Ballistite, Cannonite and Walsrode were dense smokeless; Schultz bulk smokeless. The choice of 32 grains of Ballistite is confusing, as 24 grains is the published load for a 3 Dram equivalent; 26 grains for 3 1/4 Dram.
Alfred Nobel's 'Ballistite' was introduced in 1887, patented in 1888, then ‘Sporting Ballistite’ (for shotgun shells) was patented in 1889, but not released to the trade by Nobel’s Explosive Co. until 1895. The published summary of the Trial states ‘Ballistite’ rather than ‘Sporting Ballistite’.
PLEASE NOTE that all the curves essentially meet at 6" The issue of shotgun barrel strength and wall thickness is complicated, and tensile strength is only a part of the equation for estimating bursting pressure.
Barlow's formula P=2 S t / D
P=Bursting pressure in psi.
S=Tensile strength of material in tube wall.
t=Wall thickness in inches.
D=Outside diameter in inches.
Barlow’s refers to a pipe capped at both ends with a static pressure (a pressure cylinder).
Shotgun barrels are not designed to be pressure vessels as one end is open and the pressure rises and falls quickly (milliseconds). I've discussed this issue with both a mechanical and metallurgical engineer and neither is aware of a good bursting pressure equation for shotgun barrels.
Burrard used the Alger Burst Formula:
Burst pressure = Ultimate tensile strength x 3(OD – ID) / OD + 2xID
Lame Formula:
Burst pressure psi = Ultimate Tensile strength x (OD squared – ID squared) / OD squared + ID squared
American Standard:
http://www.smt.sandvik.com/en-us/materia...rican-standard/ 
