If you don't want to slug and size your bore, try the smaller dia. bullets first. My Finn made rifle will shoot .308 up to .311's. My Russian made like .312's the best. Hornady 150 grain spitzers (.312) and 174 grain round nose (.312) are the best in my M44. My M39 likes hornady 123 grain .310" and Remington 180 grain .3105" round nose, but will shoot Sierra 150 grain .311" quite nicely.
If the smaller dia. make a shotgun pattern group try a larger dia. If you get too large you will get pressure problems at almost the starting loads and especially the round nose bullets will start coming apart (you will see several impacts in front of the target usually) and lots of recoil. Best accuracy is with a bullet the matches the bore as close as possible and with modest loads, seldom is the max load the most accurate in military rifles, the ones I own anyway.
Load carefully and have fun safely.