I've never heard of a 2 3/4 inch .410-bore shell. The .410-bore started out 2-inch that carried 3/10 of an ounce of shot, then the 2 1/2 inch was added with 3/8 ounce of shot. The 3-inch .410-bore shell was introduced with the Winchester Model 42 and carried 3/4 ounce of shot and at that same time the 2 1/2 inch shell was upped to a 1/2 ounce payload.
Many of the early tiny bore shotguns in the U.S. were chambered for the .44-40 shot cartridge or the .44 XL shot cartridge. As the .410-bore grew, from the European 12mm, some guns were chambered and bored to accept either. Many of these old guns are sold by dealers at gun shows as .410-bores, but they are really .44 calibers. At least H&R was making single barrels for these .44 shot cartridges and Sears had little Belgian hammer doubles for them in their catalogues in 1905 and 1902 respectively.