"And then compare those with the measurements I got with the Manson gauge. Anyone have any ideas on how to improve on this procedure?"
When I take wall thickness readings, I take them in 4" increments along the barrel. The Galazan type I made is a copy of one a friend has. I can measure close to 16" and then flip the barrels end for end and read the other length providing the chokes are not too full in a 12 gauge. Meaning if the muzzle end is .690 I cannot fit it over the rod. Once it is centered on the bottom brass cone, I pivot the barrel on the brass cone that is locked on the shaft from top rib to bottom rib and read the wall thickness and record the readings from lowest to highest. I then move the brass cone down another 4" and do the same until I get to where I left off from the other half.
Most of the time, the readings vary as the barrels are not concentric as most are not.
Beagle, that is a good way to prove that you are using your Manson Gage right, but you have to read the barrels as I stated and write down the areas where the readings were taken to compare them to the micrometer readings. In order to measure them with a micrometer, you will have to use a ball micrometer, or better yet a pin one to get accurate readings as a flat anvil micrometer will not give you accurate readings.
Please let us know what your results were. Also if these barrels have pitting in areas, measure some of the pits to see how deep they go.
The only micrometers my friend has are the flat anvil type, but he does have a Starrett electronic caliper. The contact edge of the caliper arms is nearly a knife edge, so I think will give an accurate reading even on a curved surface. So, on to plan B. After taking measurements at marked points on the junk barrel, cut it into segments, cutting just ahead of of the points measured with the Manson gauge. Then, after deburring, measure with the calipers and compare readings.
Don't know how I got so deep into the technical end of shotguns. Deep meaning over my head. All I wanted was a lightweight 20 to take woodcock hunting.