By and large the 12-gauge Remington Hammerless Doubles appear to be chambered 2 5/8 inches. A very few graded trap or Pigeon guns may have left Ilion chambered for longer shells, but likely not many. My Father shot a boxcar load of factory 2 3/4 inch shells thru his 1896-vintage Damascus barrel AE-Grade from the 1940s to the 1980s with no ill effects!!
Ordnance Steel would be stamped (A- or B-Grade) or engraved (higher grades)on the top of each barrel if it was Ordnance Steel. The cheaper blued Remington Steel offered on A- or AE-Grades wasn't marked. I think the steel barrels were first offered in the April 1897 catalogue.
A hang tag of 1899 vintage just states the the gun was targetted with 3 1/2 drachms F.G. Powder and 1 1/4 ounces of #8 chilled shot, but doesn't mention the shell or its length. A 1908 vintage hang tag states the gun was targetted with a UMC Nitro Club shell, 2 5/8 inches in length, loaded with 24 grains of Infallible and 1 1/4 ounces of #8 chilled shot.
On the other hand, the Remington paper on their Autoloading Gun from the very get go in 1905 states that it is made for 2 3/4 inch shells.