You CAN check the bore diameter at the muzzle if you have a .311" or .312" plug gauge. If you have a big box of Mark VII Ball ammo, then you have about 4 dozen .311" or .312" plug gauges. Defence Industries generally ran almost to .312" exactly, modern commercial stuff seems to run about .311". So that's a start, anyway.
Stand a live Ball round with the bullet in the muzzle, see how far the mouth of the casing stands out from the muzzle. On a "new" barrel, this can be anywhere up to a quarter of an inch. Get one like this and usually it is a Keeper-with-a-capital-Keep.
If it does manage to go in partway, you could still be in luck. And if the case-mouth butts against the muzzle, even then you're not toasted: worn and oversized bores often respons well to bullets with LONG shanks. The Hornady 174 is a point in case here: LONG shank and round nose.
Bullets with cannelures: you can seat them OUT, sometimes a fair bit. The Hornady Spire Points often work very well like this. For one rifle here, I seat them with the whole cannelure standing well out of the case mouth. Rifle shoots okay.
TRY 37 grains of 4895 with a Sierra 180 Pro-Hunter flatbase, seated out to the overall length of a Mark VII Ball round. This crowds the rifling just a bit and often is just super accurate.
You say the bore looks good. That's nice because if it LOOKS good, chances are that you'll find SOMETHING that will shoot well.
Keep checking in here and we'll get her worked out.
Good luck!
And congratulations on finding yourself a copy of the finest rifle ever constructed!
Pics?