The handload is the secret here, most 7,62 X 39 is roughly made(military application) and better quality components will insure precision. This round is idealy suited at short ranges (same qualities as a .30-30 Win.). You would be highly surprised to see what a hanloader can do as was described in another posting a while ago with a SKS(same caliber, yet semi-auto thus has to shorten case lenght everytime as opposed to a bolt gun).
Your best bet here would be the .270 Win.(fine caliber, super balistics, LOW RECOIL

, available thruout the world, what more do you want?
This subject was also brought up with CZ-75ID, who's already familiar with the 7,62 and opted it out for a future .270