peter is probably right, and the 20-bore 'Fauneta' cases are 2.54 to 2.58 according to George Hoyem and my own measurements, but many brass cases were 2 3/4 in length I believe. For example, the 20-bore/.577 you mentioned is formed from the 20-bore 2 3/4 inch brass rifle case necked down to .585 inch.

Personally never heard of a 3-inch 20-bore rifle cartridge from the vintage years, and neither has Hoyem apparently!