When your Parker was made in 1903, the "standard" 20-gauge shell here in North America was a 2 1/2 inch case loaded with 2 to 2 1/4 drams of bulk smokeless powder (or the equivalent in dense smokeless powder) pushing 3/4 or 7/8 ounce of shot. Longer 20-gauge shells of 2 3/4", 2 7/8" or 3" with a bit hotter load of 2 1/2 drams pushing the same 7/8 ounce load were available, but their real or perceived advantage was more/better wadding.
Parker Bros. had a policy of holding their chambers 1/8 inch shorter than the intended shell on the theory that in the days of paper shells and fiber wads the mouth of the case upon firing extending a bit into the forcing cone gave a better gas seal and hence better patterns.
All this to say your chambers, if they haven't been lengthened, may be as short as 2 3/8 inches.
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