Rob,
I shoot 2-3/4 in. shells in all my 2-5/8 in. chambered Parkers exclusively. Sherman Bell's conclusion was that as long as the load didn't generate pressure in excess of what the gun was designed for, then chamber length would not be of concern (i.e. there is a slight increase in pressure when shooting a 2-3/4 in. shell in a 2-1/2 in. chamber, but only on the order of about 10% - certainly not enough to push it over the top. And this was for 2-1/2 in. chambers, which is more of a difference than with 2-5/8 in. chambers). As for 1-1/4 oz. loads - I have shot a bunch of Kent's 3-1/4 Dram, 1-1/4 oz. loads which generate around 1200 fps and less than 8500 psi in my 2-5/8 in. Parkers. It is a great pheasant load in #6. My favorite shooter is a 1-1/2 frame -not quite as stout as your 2 frame, and it couldn't care less about these loads.