One would not expect the payload velocity vs time plot to look like the pressure vs time plot. The pressure against the base of the wad is converted to force (pressure times area of the wad base; force pounds per square inch times square inches equals force pounds). Force equals mass time acceleration. The mass is fixed, so the acceleration will vary proportionally with the force. So, the acceleration curve will look like the pressure curve. The gun's free recoil velocity and free recoil displacement will be a mirror image of the payload velocty and payload displacement scaled by the weight difference. However, when the gun is held against a human shoulder, the recoil velocity and recoil displacement are probably going to change, even though the acceleration is not changed.

The above is simple physics. How humans will "feel" it is not so simple. Or, so I believe.