With a powder chamber, the high pressure is contained in a thick walled vessel.
When the pressure moves into the large cylinder area, it should drop substantially.
I lack the motivation to do so, as I hated Statics and Dynamics and decided to become a fairly successful EE instead of an ME, but the calculation for pressure applied to the ball should be relatively simple.
Measure muzzle velocity and barrel length. force = mass x acceleration. Assume linear acceleration if you wish. Force should be guesta-calculatable if muzzle velocity is known. There will be some degree of error initially as the mass of the expanding gas hits the stationary bowling ball. I'll bet that is calculatable as well for someone that stayed with the ME degree program or someone with appropriate modeling software.
I'll stick with Ohms law and such.
The above problem could be converted into electrical parameters and I guess I could solve it using SPICE simulation program (current pulse and immovable inductance), but, well, I'll defer the entire issue to an ME.
Rick