I have rebarreled several with good quality barrels and been pleased to get MOA and less from them. However if you are just looking at shooting and not "married" to the idea of using the 7.62X54R, I'd suggest a Savage Axis in 308, or a Ruger American. Ballistics are nearly identical and reloading is far easier for the 308 in that brass is close to free, and it uses the .308 bullet instead of .310, 311 or 312.
A re-barrel job on a Mosin costs about 2/3s of the Savage rifle.
A re-barrel job on a Mosin costs about 2/3s of the Savage rifle.