Woodreaux: back on p.4 I posted an image of my set-up. Having the barrels secured with bungee cords affixed to a weighted box allows me to rotate the barrel while I'm measuring. Typically the thinnest spot is the lateral wall.
On the report I provide I document only the MWT at the points shown, but will note other numbers (or the location of significant pits seen with the bore scope) under "Comments" if needed.
"Chamber" is chamber length and diameter. The breech end of chambers of c. 1900 12g U.S. doubles is usually .809” -.812”, tapering to .795” - .798”, and unfortunately I've measured some chambers that were honed to remove pits also.

[Linked Image from photos.smugmug.com]

ed will note I have my pattern welded barrel MWT recommendations on the form. Obviously those recommendations can be discussed with the gun owner and modified depending on the barrel composition, based on incomplete but IMHO pretty good data ie. we now have composition analysis and tensile strength testing on a significant sample of vintage barrels:
Twist and Crolle Damascus tensile strength is about 55,000 psi
Winchester Standard Ordnance and other "cold rolled" Bessemer/Decarbonized steels and AISI 1020 are similar in strength at about 60,000 psi
c. 1900 Belgian sourced “Fluid Steel” used by all the U.S. makers (Cockerill, Siemens-Martin & Krupp Open Hearth) and AISI 1030 are similar in strength at 75,000 - 85,000 psi
Krupp Fluss Stahl (Homogeneous Fluid Steel) was introduced about 1890 might be a little stronger
AISI 1040 (and modified), Vickers, Cockerill Acier Universel or Acier Special & Bohler “Blitz” are similar in strength at about 100,000 psi
Winchester Nickel Steel, Marlin “Special Smokeless Steel”, Remington Ordnance Steel, Krupp “Nirosta” (1912 patent NIchtROstender STAhl 21% Chromium / 7% Nickel Stainless Steel introduced in 1913), 4140 Chrome Moly (not used until after 1930s) and 4340 (Chromium, Nickel and Molybdenum) are all similar in strength at > 115,000 psi