A relationship may exist, but the units of measure are different in pressure and velocity. One is in force per area, the other is in in distance per time.

So, it is clear that the pressure curve over time may provide some insight to the velocity.

Let me be simple and clear.. The instantaneous pressure will create velocity, but may exceed your maximus.

That pressure expended consistently over the time the projectile is traveling in the barrel, may decrease the maximum pressure while increasing the velocity.

It's hard to compare pressure units with velocity units.

But then again, I should be mowing the lawn.