The consensus on the PGCA website seems to be that Parker cut its chambers 1/8 in shorter than the expected shell length, feeling that the overlap into the cone sealed the shot charge better. Thus, 2 5/8 in chambers were for 2 3/4 in shells. That said, I shoot 2 3/4 shells at 1165 in my 2 9/16 inch 16 gauges without incident. If the barrels are sound, and the chambers original, you should be OK.
Intentionally short-chambering guns in order to improve patterns was a fairly common practice back when everyone was shooting paper hulls and fiber wads. I have a couple American Rifleman articles from the 30's that discuss it. The author had worked in the firearms industry since the 1890's. He had a 12ga Marlin 90 made with 2 1/2" chambers. Shot patterns using standard 2 3/4" shells. Then had the chambers lengthened and repeated the pattern testing. His patterns ran something like 8% better when using shells that were slightly longer than the chambers. Apparently trap shooters of that era were well aware of that and took advantage of it by making sure chambers were slightly shorter than the length of fired hulls.
Of course today, with plastic hulls and wads that do a better job of protecting the shot charge, there's no advantage to shooting longer hulls in shorter chambers. Nor, however, is there any particular disadvantage . . . AS LONG AS THE PRESSURE GENERATED BY THE LOAD IN QUESTION IS NOT SIGNIFICANTLY HIGHER TO START WITH THAN THE PRESSURE FOR WHICH THE GUN IN QUESTION WAS DESIGNED. The British regularly shoot 67/67.5MM shells in guns with 2 1/2" chambers. It works fine because those shells are loaded to appropriate pressure standards. In contrast, using off the shelf US ammo can be risky because our standard 12ga service pressure is already somewhat higher than the CIP (British/European standard)--by about 800 psi. Add to that the fact that Bell recorded increases in pressure that were mostly only a few hundred psi, although in one case the pressure increased by more than 1,000 psi.
Result: If you're shooting a 12ga and reloading standard American 2 3/4" hulls through a gun in good condition, you shouldn't have a problem as long as you build in a safety margin. It's very easy to come up with reloads, for shot charges up to 1 1/8 oz, at pressures under 8,000 psi.
