Before I invested in a rechamber job, I'd try the old 6" scale method. The chamber may be a "Bit Tight" rather than short. To do this if you don't have one buy one of those little 6" metal flexible scales from your home improvement store for about $3.00. Hold your bbls up toward a window or other light (but not with the sun on it) & look down the bore until you see the forcing cone as a shadow. Slide that scale in beside your face holding one edge against the chamber wall where-ever is convenient to see. Slide it in till the corner just touches the shadow. You won't feel it, but can see it. Mark the scale at the breech & read the depth. Repeat a few time to insure you are being consistent. With just a wee bit of practise you will find you can consistently measure the chamber length to the smallest graduation on one of these scales, which is plenty accurate.
As a chamber body has about .005" taper per inch should the end of the chamber be only .001" smaller than the dia of a precision gage made up to SAAMI specs it will indeed stop .200" short. In talking of guns of this age tolerances may well have been a little looser than today. Unless that gage just happens to be a perfect match in dia to the small end of the chamber the scale can actually be the more accurate method of measuring it.
As 2½" was never really a standard length for 12ga shells in the US & trap shooters were more prone to using the longer hulls for a better wad column, I seriously doubt the gun was designed with 2½" shells in mind.