Plan B or C or D.....To each their own but I would NOT ream out the chamber on any gun or otherwise mess with dimensions on an old classic, whether American, British, German or whatever. As many others have noted, there are newer LC Smith guns with 2-3/4 chambers. As for lighter loads, some are available in general from Gamebore, RC, RST and others. RC tend to be the most affordable and they actually publish their pressures. Unless the gun has been re-proofed by a proof house a suitable for modern loads (NOT STEEL), I would not run anything from Walmart etc through it. Forget the gun....I value my fingers and my vision. I have a number of old gun - some as old as the 1880s but most in the 1920s-1930s from England and Germany. All function perfectly with proper loads (see above) and easily kill pheasants in reasonable range. Yes, you are limited on waterfowl unless you spend upwards of $50/box for bismuth. I do not generally use these for clays except for modest outings - 25 or 30 shots for tuning up) - this will change as I can finally get into reloading lighter loads.
Bottom line, if you are set on an LC Smith, find a newr one in 2-3/4, check for proof marks and for stock and barrel condition and if possible have it checked by a KNOWLEDGABLE gunsmith before consumating teh purchae. Otherwise consider any of the really wonderful other SxSs from England, Germany, Belgium or Italy. FYI, another source for primairly German guns is Save the Fine Guns - reaonable prices on impoted older primary German guns that HAVE been checked over by a German gunsmith prior to sale.
Good luck on your quest - it really is satisfying to pull out a 100 year old gun in a field of black or camo autoloaders and proceed to bring home some birds - light, beauticul, unique and back in the field where they belong!
Below is a Charles Boswell, action from 1870s, Damascus barrrels from 1880s; 6.5 lbs, chambered in 2-3/4 and proofed in 2011 for modern light loads. Kills birds dead and pretty hard to find anything as beautiful in the field these days. Runs RC shells and some Lambro with no issues at all.