Burrard's The Modern Shotgun, Vol. II "The Cartridge", 1955 3rd Edition has very little about 2" guns or cartridges, and no mention of Lancaster's Pygmies
p. 157 lists standard pressures for cartridges
12g 2 3/4" Service 1 1/4 oz. 3 1/4 Dr. Eq Service 3.1 tons = 9,296 psi; Max. 3.9 tons = 11,984 (by his conversion to piezo number)
12g 2 1/2" 1 1/16 oz. 3 Dr. Eq. Service 2.7 tons = 7,952 psi; Max. 3.5 tons = 10,640 psi
12g 2" 7/8 oz. 2.36 Dr. Eq. (26 grains of 33 grain = 3 Dr.Eq. powder) Service 2.25 tons = 6,440 psi; Max. 3.0 = 8,960 psi
Vol. III also has very little
p. 217
"The 2-inch 12-bore...was originally introduced as an alternative to the 20-bore and fired the standard 2 1/2-inch 20-bore shot charge of 3/4 ounce. Experience proved that this shot charge was too light. So the shot charge was increased to the standard 2 1/2-inch 16-bore weight of 7/8 ounce."

SO this would support Brent in that 2" loadings at some point after 1934 were changed to lower oz. & pressures than the standard 12g 2 1/2" load, and Burrard's numbers would provide a good guide regarding load pressures.

Bill's Titewad load is approaching, but not reaching, the max., but as Brent stated, Boyle's Law would suggest higher pressures if the test barrel had a 2" chamber