Carpetsahib,
Not sure of your formula of the goings on in the barrel, but your thoughts on chamber pressure are spot on. If its 44,000 psi inside the 450 nitro, then its that pressure per square inch of inner surface area. you could weld a garbage can lid to the end of the round and it would still be 44,000 psi inside the round and if the inner area is .462 then back thrust is a function of that area, otherwise, as in my example the back thrust of the garbage can lid welded would be in the area 345,000psi against the breech.
John