The Remington era Parker specification sheets reproduced on pages 164 to 169 of
The Parker Story call for the "normal" Parker 20-gauge chamber to be 2 5/8 inch intended for the 2 3/4 inch shell. "Other chamber depths optional"
During the years that Parker Bros. offered 20-gauge shotguns, the "standard" 20-gauge shell in North America was put up in a 2 1/2 inch case and the maximum load was 2 1/4 drams of bulk smokeless powder or 18 grains of dense smokeless powder such as Infallible or Ballistite pushing 7/8 ounce of shot. Longer cases -- 2 3/4, 2 7/8 and 3-inch -- were offered by our North American ammunition companies
3-inch IDEAL 20-gauge.jpg
and one could get a slightly hotter load of 2 1/2 drams of bulk smokeless powder or 20 grains of dense smokeless powder such as Infallible or Ballistite pushing that same 7/8 ounce of shot.
Remington Arms-Union Metallic Cartridge Co. Arrow 3-inch 20-gauge.jpg
The main advantage of these longer shells was more/better wadding which many serious shooters considered important.
In 1922, Western Cartridge Co. introduced their progressive burning smokeless powder, high velocity, loads, Super-X, in 12-gauge (1 1/4 ounce) and 20-gauge (1 ounce), put up in their 2 3/4 inch FIELD shell.
Early Super-X 20-gauge box, Super Excellant.jpg
Parker Bros. didn't rush to embrace the 2 3/4 inch 20-gauge shell. My 1930 vintage VH-Grade 20-gauge has the 2 3/8 inch chamber intended for the 2 1/2 inch shell.