Gents,
The general principles of regulation are very well known due to double rifles, which have far more ambitious goals for regulation than shotguns ever will.
Regulation depends on:
- construction of the barrel set (static convergence, length of barrels, straightness, muzzle area)
- projectile velocity profile in the barrel (charge of powder, type of powder, projectile characteristics, friction on the barrel walls)
- inertia of the gun + projectile (how much does it move while the projectile goes down the barrel)
- to a lesser extent, how you hold the gun (same as above)

Even though indeed the tubes should be straight through manufacturing, I am sure that someone somewhere fixed up regulation by mucking with the barrel assembly.
Pretty much *all* double rifles are done this way : the breech and the forend loops impose a fixed geometry on the barrel assembly towards the breech, and only the muzzle wedge is adjusted to make things work. The barrels *have to be bent* (in a small way)to make this work.
Another way is to modify the muzzle profile. This is heretical to double rifle people but well known recent examples exist.

By and large, the shotgun makers should know how to build a shotgun to make this work without mucking around with anything post assembly in a "correct by construction" methodology. Of course, the way you define correct is interesting, i.e. how good is good enough...
Additionally, the regulation cannot be perfect for every load anyways.

Best regards,
WC-