Three-inch shells have been around just about as long as cartridge shotguns have been around. Prior to repeaters, which needed a certain length shell to function reliably, there were a plethora of shell lengths. In my 1903 UMC catalogue there were 12-gauge paper shells 2 5/8, 2 3/4, 2 7/8, 3 and 3 1/4 inch. The 16-gauge was available 2 9/16, 2 3/4, 2 7/8, and 3 inch. The 20-gauge was offered in 2 1/2, 2 3/4, 2 7/8, and 3 inch. In those days these longer shells didn't pack a heavier payload, but more and better wadding for a better gas seal which many serious Pigeon shooters thought to be an advantage. The first time I see the longer shells packing a heavier load was around 1912 for the 3-inch 20-gauge for the famous Widgeon Duck Club Parker Bros. guns and the J. Stevens A & T Co. pump gun. These 3-inch 20-gauge shells packed 2 1/2 drams equiv and 7/8 ounce of shot as opposed to the max load of 2 1/4 drams equiv. and 7/8 ounce of shot in the standard 2 1/2 inch 20-gauge shell! These shells were loaded with dense smokeless powder measured in grains (the heaviest load of ballistite offered in the 2 1/2 inch 20-gauge shell was 18 grains) while the longer shells could be had with 20 grains.
Several of the early Ansley H. Fox graded 20-gauge guns, circa 1912-13 were chambered for the 3-inch shell of that period.
By the late 1920s, Peters Cartridge Co. was offering their High Velocity progressive burning smokeless powder loads in long cases for about $10 per thousand more. From 1927 Peters catalogue --
This box is from the early 1930s in that it has Rustless priming, but pre 1934 as no DuPont markings --
