There's a good bit of speculation about the 3 1/4 inch case and its origins. I personally think that Sharps did introduce it probably just before they closed the doors for the last time. There are in fact letters from the West asking for just that very thing, but the standard factory answer was we already load the 2 7/8 in case with 120 grs of powder and the 550 gr patched bullet.
In the Sharps catalogs they do indeed list the 120 gr load in the 2 7/8 inch case.
Lots of fun and good reading if you go to Cornell Publishing and order the reprints from the Sharps, Remington, Winchester, Marlin and others from back in the day. Those things are a gold mine of information.