Thankfully I've saved this as a word document and don't have to retype it!!
16-Gauge History lesson --
From the late 1890s until after WW-I, the heaviest 16-gauge loads our North American ammunition companies offered were 2 3/4 drams of bulk smokeless powder or 22 grains of dense smokeless powder such as Infallible or Ballistite, pushing 1 ounce of shot. Those loads could be had in the "standard" 2 9/16 inch case or any of the longer 2 3/4, 2 7/8 or 3-inch cases. So, at least in factory loaded cartridges, the longer 2 3/4, 2 7/8 and 3-inch 16-gauge shells only benefit was more/better wadding.
In late 1922 or early 1923, Western Cartridge Co. added the 16-gauge to their progressive burning powder loads called Super-X, but unlike the 1 1/4 ounce 12-gauge and 1 ounce 20-gauge Super-X loads which were put up in Western's 2 3/4 inch FIELD shells, the 1 1/8 ounce 16-gauge Super-X load was put up in their 2 9/16 inch FIELD shell. When the Lubaloy shot Super-X loads were introduced in July 1929, they were put up in Western's high brass RECORD shell, but the 16-gauge still in a 2 9/16 inch length case.
The 2 3/4 inch 16-gauge shell really began to get some traction when Remington Arms Co., Inc. introduced their Model 11 and "Sportsman" autoloaders in 16-gauge in 1931, chambered for 2 3/4 inch shells. While Remington's regular Nitro Express 16-gauge progressive burning powder load was put up in a 2 9/16 inch hull with a load of 3 drams equiv. pushing 1 1/8 ounce of shot, for their new 16-gauge autoloaders they introduced the slightly faster Auto-Express with a 3 1/4 drams equiv. charge pushing 1 1/8 ounce of shot --
I'm thin on Winchester ammo catalogues, but for sure by 1934, they were offering a similar 2 3/4 inch 16-gauge load.
The 2 3/4 inch Magnum shells with 1 1/2 ounce in 12-gauge, 1 1/4 ounce in 16-gauge and 1 1/8 ounce in 20-gauge first appear in the December 15, 1954, Western Cartridge Co. catalogues.
Western Cartridge Co. added a 2 3/4 inch 16-gauge to their Super-X offerings for 1938. From 1938 through 1942 they called this 16-gauge 2 3/4 inch Super-X shell "Magnum", even though it was still a 1 1/8 ounce payload. By Western Cartridge Co.'s March 7, 1946, catalogue the term "Magnum" was gone from this 2 3/4 inch 16-gauge Super-X shell. In Western's January 2, 1947, catalogue, the 2 9/16 inch 16-gauge Super-X shell was gone from both the chilled shot and the Lubaloy offerings, and their only 2 9/16 inch shells being offered were Xpert. This may have been an oversight, as the 2 9/16 inch 16-gauge Super-X shell with chilled shot is back in Western Cartridge Co.'s April 8, 1948, catalogue and price list, and the 2 9/16 inch 16-gauge Super-X loads remained until their last appearance on Western Cartridge Co.'s January 2, 1962, catalogue and price lists, where it is "available until stocks depleted." By Western Cartridge Co.’s January 2, 1963, catalogue and price lists the new Mark 5 was introduced and all the 16-gauge Super-X offerings are 2 3/4 inch. By the January 2, 1964, Western Cartridge Co. catalogue and price list the 16-gauge 2 9/16 inch Xpert shell is gone as well.
With Parker Bros. policy of holding chambers about 1/8 inch shorter than the paper shell they were intended for, the "standard" Parker Bros. chamber for the "Standard" 2 9/16 inch 16-gauge shell of 1907, would have been 2 7/16 inch, probably what you are measuring as 2.5". A gun made for the 2 3/4 inch shells would have a 2 5/8 inch chamber, etc.