I double checked my math. What I said was "Close" was to take Pi x D using the mid point diameter as D. For my double check I figured the area of a .740" diameter minus the area of a .730" bore. An old Machinery's Handbook gives the weight of steel (No specific alloy given) as .2817 lbs per sq inch. I rounded to .282 lbs/sq/in. Using the same criteria of estimating that about 22.5" of both barrels would be enlarged & then converting lbs to ounces it took 9 decimal places before there was a difference in the two methods.
The simpler method of using pi x .735" x .005" thickness gave 2.344168473 oz.
Using the area of .740" minus the area of .730" with all other criteria the same gave 2.344168474 oz. That is thus the amount of weight you would be looking at in removing .010" of steel from the bore of a nominal 12ga bore. Considering bore sizes normally found in 12 gauge guns & for a 26" barrel length you are looking at the range of 2Ľ to 2˝ oz for a .010" enlargement.
Rich, I know what you mean by that "Special Feel". To me my Birmingham built J P Clabrough has it. It has 28" Damascus barrels with a weight of 6lb 14oz & carries Nice. I have also however done some good shooting, For Me, with a 7˝ lb FE Lefever which had a set of 26" steel barrels built which match the weight of the original 30" Damascus ones. These barrels were built from scratch so I still have the originals.
