What you are not looking at here is the Time factor. Which will flex the standing breech the most 6K psi for X Microseconds or 8K psi for Y Microseconds.
Your formula while certainly true does not truly address this for such a short duration of time.

Explain by Pascal's Law why a lead crusher does not give the same pressure reading as a Piezoelectric crystal, the same pressure is applied to both.

Let's turn this around & say that if I have two loads both producing 8K PSI. One load uses 1¼ oz shot @ 1330 FPS while the other uses 1 oz shot @ 1130 FPS. As I understand what you are saying from Pascal's formula both would stress the action identically. Both should thus have Identical Recoil, I think we all know this is simply not true. Another "Law" states for Every Action there is an Opposite & Equal Reaction". The Reaction of 1¼ oz of shot 200 FPS faster is simply greater than the 1 oz load even though pressures are identical. "IF" on the other hand the payloads & velocities are identical then the Reactions are identical even though the pressures are different. The total picture simply has to be looked at.


Miller/TN
I Didn't Say Everything I Said, Yogi Berra