I think that you are correct about the pressure numbers, but need to think of the application? So, SAAMI sets service load pressures in the range of 11,000 psi through to about 14,500 psi for various gauges - I could not find SAAMI's "proof pressure" levels, but CIP has general principle of 1.25 the maximum service pressure - so, I am presuming that a modern smokeless shotgun is "proofed" to 14,500 psi x 1.25 = 18,125 psi for a 3.5" 12 gauge - about the highest "service pressure" that that I could find listed. Most other cartridges lengths and gauges seem to be less than that. I looked in the Lyman Black Powder Edition 2 - so p. 268 - for 58 cal - loads listed from 9,300 psi and less, on up to 18,000 psi. So, from that, there are published black powder loads, with conical bullets or ball, that likely exceed the "proof" level pressures used to "proof" a lot of smokeless shotguns with various cartridge lengths and gauges.
And for sure, that Lyman book shows many muzzle loaded BP loads for shot between 1,300 psi (p. 297) and 5,600 psi (305). Gets to be a bit "heavy slogging" between "psi", "CUP" and "LUP" and whether for lead shot or steel shot, and what was used for wads and cards, and which brand of which granulation of black powder, and so on... It might be like loading smokeless shotgun - pressure levels that are "safe" versus where the shotgun comes apart are not apparent to the home guy with no pressure testing gear - just different than the centerfire rifle cartridges that many of us "work up" loads for - there is no "working up" in the very low shotgun pressure ranges.
OP - I re-read your Post #7 - has to be muzzle loading, you want shot, not ball, and want a double barrel. Multiple loads given in that Lyman Black Powder book to do that in a 26" barrel 12 gauge with Modified Choke, but most shot was #7 1/2 through to #2 - I did not think shot size mattered, although weight of the payload does - maybe about getting it to fit?? - and then p. 306 shows using .690" ball in a 12 gauge muzzle loader, with Modified Choke, to max velocity of 1175 fps. No mention that I could find about the forcing cone thing - but for sure many "warnings" about not having "air space" between the black powder and the payload.