I just dug my FE Trap Gun, very close in age to your BE-Grade, out of the safe and my Galazan gauge shows the same as yours. Using my preferred machinist scale method I get right on 2 3/4-inch.
The hang-tags that have surfaced for 12-gauge Remington Hammerless Doubles show them targeted with UMC SMOKELESS or ARROW shells Load No. 8 and later NITRO CLUB Load No. X8. That load is 3 drams of bulk smokeless powder or 24 grains of dense smokeless powder such as Infallible or Ballistite pushing 1 1/4 ounces of shot, usually #8. A 1902 vintage tag --
319322 03 Hang-Tag front, SMOKELESS 2 5-8 inch.jpg
A 1905 vintage tag --
131920 01 front, ARROW Load No. 8, 2 5-8 inch.jpeg
A 1907 vintage tag --
135127 00 hang tag 1907 vintage, NITRO CLUB Load No. X8, 2 5-8 inch.jpg
A 1908 vintage tag --
372340 KE hang tag early 1908 vintage, NITRO CLUB Load No. X8, 2 5-8 inch.jpg
All the hang-tags I've seen say 2 5/8-inch shells including a 1910 vintage (139973) that is too blurry to post. The rub is that by 1907, our U.S. ammunition manufacturers had quit offering 1 1/4-ounce 12-gauge loads in the 2 5/8-inch shell. From then until WW-II only 1 & 1 1/8-ounce loads were offered in the 2 5/8-inch case and you had to go to a 2 3/4-inch or longer case for 1 1/4-ounce 12-gauge loads. From the UMC 1907 catalog --
1907 NITRO CLUB loads.jpeg
When Remington Arms Co. introduced their John M. Browning designed Remington Autoloading Shotgun in 1905, it was made for 2 3/4-inch shells. Would they continue chambering their doubles for shorter shells? Likewise, when they introduced their John D. Pedersen designed Remington Repeating Shotgun in 1908 it was made for 2 3/4-inch 12-gauge shells.
Threaded Mode