Stan et al;
When I read your post yesterday I thought about responding straight away, but as I knew this post would generate significant interest and comments I wait until now.
Firstly, let me say that my experience is gained from restoring English shotguns and building double rifles, most recently the building of a double rifle using the "shoe lump" method used by the likes of Verney-Carron and Heym. If you are not familiar with the shoe lump method of attaching the lumps to the barrels, view one of the Verney-Carron videos on You Tube to see how the shoe lumps are brazed to the barrels.
Secondly, let me say this is not my first rodeo, as I am 75 years of age, and began my interest of above in the early 1960's.
It has been my finding that it is most common to find a double shotgun of common quality where the face of the action is not square with the center slot. The center slot of a double gun/rifle action is the datum where every other measurement of an action should be referenced. For each action that I use where I build a double rifle I build an individual precision test mount that fits into the action middle slot from the bottom of the action. The test mount with the action securely attached is placed in a milling machine and and the action face is measured via instruments to determine if the action face is square to the center slot. If the face is not square to the center action slot, I mill it square before starting my work. I work from left to right measuring the action face. The current action that I have just used to build a DR was 0.009" left to right out of square with the left starting point being set at 0.000". I have found an action that had 0.017" out of square runout across the face.
Now of course, when the action is out of square with the center slot, a set of barrels with the lumps made to fit into the action center slot will have to be faced "off square" to the barrel lumps, which in and of itself is not a difficult task for a gunmaker. However, when the gunmaking process is "machine made" a tolerance measurement will be used in fitting the barrels "to face". This tolerance will have a +/- range and some guns will be finished very tightly on face and some more loose on--but all within good engineering practices.
Specific to your out of face gun, clean the barrel hook with laquer thinner and apply one piece of aluminum or magic mending tape to the barrel hook to determine how many thickness of tape required to tighten the action to the barrels. Aluminum tape used by HVAC techs is the best for this exercise. Of course, measure the thickness of tape with a micrometer before you begin.
Remember that if the action is 0.004" off face, it is reasonable to expect to have to make a new hinge pin 0.009" to 0.012" larger diameter as some metal will be required to scraped from the hook to fit the new diameter hinge pin.
