North, I've got a few thoughts/ideas,

-As pointed out, bump up a round ball by smacking it with a hammer a few times so you have to gently drive it through the bores then measure. Do it with both barrels and from both ends. My ~1870 10-bore is choked ~.003 for the last few inches. I only discovered that when slugs tapped in the muzzles fell freely toward the chambers after just a few inches of tapping yet had to be driven firmly all of the way from chamber towards the muzzle.

-The proof marking shows the size of the largest measuring gauge that would pass freely through the bore and is usually one "size" under the actual size for a rifle. Put another way, if 10-bore=.775" and your gun is marked 11, it means the bore is smaller than .775" land to land but bigger than .751". It could well be .774" or even be larger than .775" groove to groove. My .778" 10-bore is proofed 11, my 4-bore is proofed 5, and I owned an 8-bore that was proofed 9.

-My light ~10lb 2.5" cased gun is marked 5 drams. I'd guess your 2 3/4"gun is made for 5-7 drams depending on weight, as the barrels look trim. If it's in the 13+lb range the charge might be heavier, but then the case would probably be longer too. From the slow twist I suspect it is a roundball gun.

-I absolutely swear by a lubed felt wad at least 1/2" thick above the over powder card. I melt wonderlube or similar black powder lube in a shallow tray like a styrofoam meat tray in the microwave then roll the edges of the wads in the melted lube and store them in zip lock bags. They compress and give a complete powder seal (unlubed ones in tests show burned edges) and can let you get away with slightly undersize bullets or inconsistent groove depth without worry of blow by. They can compensate for a ton of variables.

-Lastly, try every type of powder you can get. My Tolley was made for 700 grain balls at 1300fps per their original advertisement. I tried loads from 1100-1450 fps in brass and plastic cases, with and without crimps, with blue dot, goex Fg, FFg, and FFFg, in almost every possible combination and never got a pattern better than crossing 8" at 30 yards, probably why I got te gun at a good price!! I happened to find a can of Swiss FFFg at a gun show and decided to try a reduced load of just over 4 drams with a heavy roll crimp in a plastic case and heavy cards. Load #36 gave exactly 1300fps and the holes consistently touch at 50 yards! It is now my favorite rifle.

Please keep all of us posted. Thanks!

Bob