Results are in, and I found some additional information
From a 1934 Winchester salesman’s manual reproduced in The Rifleman’s Rifle Winchester's Model 70
“Proof Steel. Winchester pioneered the alloy steel field by the production of heat treated nickel steel barrels thirty years ago…”
“Two or three years ago our metallurgists together with those of one of the greatest steel companies in the country, produced a new alloy. This new alloy was a chrome molybdenum steel which was capable of being tempered to a greater strength and resistance to wear, and still be in a machinable state, than any other alloy yet discovered.”
“Winchester decided to coin the name ‘Winchester Proof-steel’ which would be Winchester’s guarantee that it would be the finest alloy steel known at the time.”
The Winchester Model 12 owner’s manual in the 1960s state “Only the finest of gun steels-WINCHESTER Proof (Chrome Molybdenum) Steel-is used in the manufacture of your Model 12.”
Winchester catalogs in the 70s state Proof Steel was “cold forged Chrome Molybdenum”. Winchester's Finest The Model 21
by Ned Schwing states Chrome Molybdenum alloy.
Mike Hunter has stated specifically 4140.THIS
1937 Model 12 “Winchester Proof Steel” barrel is non-standard (low chromium and slightly high molybdenum) AISI 4135 medium carbon low alloy steel
Carbon – .34% (0.33 - 0.38)
Manganese - .76% (0.7 - .9)
Chromium - .62% (0.8 - 1.1)
Molybdenum - .30% (0.15 - 0.25)
Nickel - .09% (< .01)
Yield strength – 79,500 psi
Ultimate tensile strength – 107,000 psi
% elongation – 12
(Industrial standard for non-heat-treated 4135: Yield – 75,000; Ultimate – 110,000 psi. 4135 may be heat treated to much higher strength.)
I recognize that Winchester over the years may have specified 4140.
And BTW I was not able to find a definitive statement as to which company made 1930s "Winchester Proof Steel"
I also have no explanation for the internal barrel defects, the ring bulge, and the crack.