I have a book named "PARKER America'. Finest Shotgun" by Peter H. Johnson. In a section he titles targeting, he explains Parker's process for targeting their barrels.
All the barrels were sent to the "shooting room" where they were locked into a fixed rest, aimed, and fired at a 30 inch diameter steel plate at 40 yards. The barrels were re-bored or straightened until they patterned dead center at 40 yards.
As stated above, I doubt this much effort is put into any gun currently made. Also, technology should have come up with something more efficient by now. However, I think this is a good example of how doubles should be set up to shoot. Correct terminology or not, this is what I visualize as convergence.
If the two patterns are seven inches apart at 16 yards, there is something definitely wrong, at least in my opinion. I could be the regulation, or the choke. Using the Parker method as an example, I would think an aimed pattern would center just right and left of your aiming point at 16 yards from the respective barrels.
Hope this helps,
Milton