None of my collection of old ammo catalogues and literature offer a 3-inch 16-gauge shell much after WW-I. Where did the 3-inch shells for those few Model 21 16-gauge guns with 3-inch chambers come from? The one offering of a 3-inch (or 2 7/8 inch) 16-gauge shell I find in the years of the Model 21 is a footnote at the bottom of the Winchester Leader page in the 1934 Winchester catalogue #89. None of the other 16- or 20-gauge shells are offered in extra-length cases, Leader Super Speed, Repeater Super Speed, Repeater, Ranger, or NuBlack. The 3-inch 16-gauge shell Stadt shows on page 159 of his book is a Leader. The only 16-gauge load given for the Leader shell is 2 3/4 dram equiv. of standard smokeless powder and 1 ounce of shot. Meanwhile the Super Speed 16-gauge is offered in either a 2 9/16 or a 2 3/4 inch shell with a max charge of progressive burning powder and 1 1/8 ounce of shot.
Best bet is to watch Wards auctions --
https://www.wardscollectibles.com/