In looking at a lot of high speed photographs, I cannot recall one where there was any apparent movement of the barrels before the projectile exited the gun, other than with a very few large caliber handguns. And they went up. I suspect the phenomena may be much more pronounced in guns with thin barrels, but I don't really even know if it exists.
I am sure someone could work out the mathematics of the whole thing. I'm an engineer but I just don't have the energy any more. Al long as the shot hits where I want it to I don't really worry too much about the esoterica. In fact I try NOT to worry about such.
