Just like the 12- and 20-gauges, from the get go in the 1880s and 90s a number of different length 16-gauge shells were offered. Into the 1930s the "standard 16-gauge shell in North America was 2 9/16 inch, but 2 3/4, 2 7/8 and 3-inch lengths were offered. This is from the 1927 Peters Cartridge Co. catalog --
From the 1901 UMC catalog --
In those days the extra length 16-gauge shells didn't offer any heavier loads then could be had in the "Standard" 2 9/16 inch shell, but did offer more/better wadding which many gun cranks thought significant.
The first time I've found a longer 16-gauge shell with a "hotter" load, came in 1931 when Remington Arms Co., Inc. introduced their Model 11 and "The Sportsman" autoloaders in 16-gauge made for 2 3/4 inch shells. Their regular progressive burning powder, high velocity, 16-gauge NITRO EXPRESS load was 3 drams equiv. pushing 1 1/8 ounce of shot. For their new autoloaders and other 2 3/4 inch chambered 16-gauge guns they introduced their AUTO EXPRESS load of 3 1/4 drams equiv. pushing that 1 1/8 ounce of shot --
If memory serves me correctly it was in the late 1970's I was at my favorite gun shop of the time & a gentleman brought in a fired 3" 16 ga Remington Express SP hull he had found while deer hunting. He was in the mountains in one of the few areas in TN that holds a few grouse, so was possibly used for one of them. It was marked as 3 de-1˝ oz #7˝ shot as I recall.
If such a shell exists, it was never a catalog item. Possibly something they were experimenting with?!?