It has been previously stated here on the board that Parker delibretly chambered their guns 1/8" short for the intended shell length. Many of the earlier guns were no doubt intended for the 2 5/8" shell. By 1910 I highly suspect most Parkers were intended to be able to handle the 2 3/4" shell, definitely so by 1920.
I can in no wise prove it, but also highly suspect they just continued chambering to 2 5/8" & stated the guns were built for 2 3/4" shells. In any case placing a 20ga hull inside a 12ga one will not detect a short chamber "UNLESS" the chamber ends in a distinct step which I have never seen a chamber so cut. I do though understand a few Very Early shotguns had such chambers.
Put the 20ga inside the 12ga but leave it protruding about an inch from the end of the 12 then insert it into the chamber & see how far it is pushed back into the 12ga hull. This will show just how far the 20ga rim will enter the cone & very quickly point out the fallacy of this method.
Note also the head of the 20ga hull ahead of the rim is not a tight enough fit in the 12ga hull to give you any more feel of the chamber end than just using an empty 12ga hull alone.