at SAAMI pressures, the max breech thrust for the 357Max is still only about 3/4 of a 12ga 3" and only 62% of the 3 1/2" that is available on a Pardner SB1
I think your fears are unfounded
even a 3030 is less than a 12ga 3"
the 30-40Krag is about equal to a 12ga 3"
and how many guys have rechambered their SB1 44mag to 445supermag, which runs 9,800lbs breech thrust, or just a hair under the 30-06 at 10,360lbs
the 22-250 is about 1/3 greater than the SB1 Pardner 3 1/3 12ga.
will that produce a catastrophic failure? I doubt it, but I would not be surprised if it started to stretch the frame, and wreck the gun.
a rifle powder is slower than a shotgun powder, and steel IMO seems to stand up better to slower stresses than quicker stresses, but the elastic limits are stressed more with the longer dwell time, and that is where the danger lay.