The SAAMI meeting where it was "suggested" that manufacturers start marking the chamber length on their shotguns was in 1937. In their 1938 Fox catalog, Savage began stating "Chambered for 2 3/4 inch shells in the text for each grade. Some 1938 vintage guns, and all 1939 and later have this roll-stamped on the barrels --

Similar markings appear on earlier A.H. Fox guns that were back to Savage for repairs.
Same thing on my Remington pumps and autoloaders. Up into 1938 they are just marked with the gauge --

I don't have a 1939 or 1940 Remington but from 1941 on the markings include the chamber length --

Ithaca seems to have been very hit or miss on marking chamber lengths. I have seven NIDs and only the 1935 vintage No. 1 28-gauge is stamped 2 7/8 CHAMBER --

The latest NID I have is a 1940 vintage 16-gauge No. 4E and it is not marked as to chamber length.
Ted, Your gun must be right near the end of the early-style Nitro Special frames --

during 1937 vintage serial numbers we begin seeing the use of the A-Grade style frames for Nitro Specials --