You cannot accurately generalize higher pressure to a corresponding equation in velocity.
Well, I said as much in my post, right? Are you just trying to be contrary?
I will still stand by that - pressure does not equal velocity, but, they are closely related.
The only thing to consider (within the same gun) is the dynamics of the pressure application, rather than just a single instantaneous pressure number. But I already said that too.
The bottom line is - the reason the bullet is traveling at said speed when it exits the muzzle is that is has had a (somewhat time varying) force applied differentially to it. That force, at any instant in time, is
exactly proportional to the pressure behind it, which is essentially the same everywhere behind it, since it is exerted in all directions. That's the most important physics of the situation, and to argue that a second order effect (the dynamics which only modulate in time, rather than actually change the above fundamental relationship) somehow trumps that, in my opinion, puts the cart before the horse.