The SAAMI standard for cartridges marked 2 3/4" is 2 5/8" to 2 3/4". Many major cartridges will measure 2 5/8" expanded. Winchester AAs tend to be short.

Most major makers also sell 1 oz 2 3/4 dram loads. The standard trap load since the 1880 s has been 1 1/8 oz 3 drams , providing 1200 fps so there are many suitable loads for your gun. The 1 1/4 oz 3 1/2 dram loads will exceed maximum recommended service loads. You will need to determine the soundness of your vintage gun .

If you want to learn about the strength of Damascus barrels, study Dr. Drew Hause's thread in the Damascus barrels section. Unless honed thin, they are sufficiently strong for any reasonable load.

Many gun makers back when you gun was manufactured made the chambers a bit shorter than the shell. They thought it would help seal the burning powder better with the fiber wads that were used. You'll find many 2 9/16 or 2 5/8 chambers meant for 2 3/4 shells. It's also why the forcing cones [ right in front of the chambers ] were shorter than todays with the plastic wads. The fiber wads were about 5/8" [ 1/2" cushion and 1/8" overpowder ] , so the shorter 5/8" forcing cones were used. Because I reload at about 7000psi, a low pressure load, I've never measured any of my guns chambers. All of them are Damascus except two, and I shoot clays three times a week year round. Bruce has said what Parkers were proofed for, so just shoot your gun and have fun.