Then, if the gun has no rear sight, make a temporary one. Then shoot groups using your right eye, and shoulder, and then with your left eye and shoulder off the bench. That will eliminate any problems with shooting form as the cause of the different POI.
If the results remain the same, try adjusting the powder charge, and then the patch thickness.
For example: I saw a half inch upward change in POI in my 50 cal. rifle at 50 yards just by using a vegetable fiber wad between the powder and my PRB. The powder also burned more completely, indicating a rise in pressure and temperature, and an unknown(yet) increase in velocity. I will probably increase the thickness of my patch after doing more testing. I would prefer to NOT need that vegetable fiber wad when loading in the field.
The last thing to do is file the barrel. Just don't get any idea that you will file it so much that anyone will notice, looking at the muzzle, unless you point it out to them.
Just a thought: That HUGE, heavy, 12 ga. ball puts a lot of WHOMP on any wild game, from deer to Grizzly bear. I find it very difficult to think of any game I would shoot with your gun that would require a second ball so fast that I would load the second barrel with another ball " Just in case". The exception might be bear, and wild boar, as both have been known to charge hunters. But, for that reason, a 12 ga. smooth bore shotgun without a rear sight would NOT be my choice of firearms to take either species.
What I am thinking is, -- with that right barrel delivering its ball to your point of aim, what more do you want??? :hmm: Most hunters using a single barrel shotgun to hunt game that can send a large, lead ball to their point of aim would think they died and went to heaven!
I have filed the muzzle of a Dbl. shotgun (12 ga.) to regulate shot patterns, not RB. Its an old shotgun and family heirloom that had to have its barrels cut to remove a deep scratch from one of the barrels. The process of regulating the barrel to strike the same POA is the same for both shot loads, and for RBs.
However, you do need to decide if you want to use this gun exclusively for RBs, or only shot, or both. Regulating two barrels to send balls to the same POI does not guarantee that the same barrels will send shot patterns to the same POA. :hmm: