Been shooting Boxer-primed 7.62x54R, head stamp = JMS 02 (170gr FMJ-BT) to fire-form the brass for reloading. Now have several hundred cases, tumbled and decapped. The rifle (Finn M28-76 with original aperture sights) is getting tolerable accuracy at 300 yards, but I want to see if reloading might tighten the group. Bore slugs at .310. Should I start with a .311 projectile?

I would

A 308 bullet will not shoot at all in that bore, and a 310 may not be much of an improvement. I would look for the larger bullet.

The 303 bullet is a 0.312". That may work well as long as the case neck can expand and have clearance between it and the bullet. If the chamber neck won't let the case expand, but rather pinches the bullet, that will unpredictably raise pressures.

For your best accuracy you do want to use .311 and .312 diameter bullets.Pressure will not be a problem with either bullet.
Don't waste you time and money with .308 bullets.

quote:

is getting tolerable accuracy at 300 yards,

The first question I have is what is tolerable accuracy.

quote:

Originally posted by p dog shooter:
The first question I have is what is tolerable accuracy?

Tolerable accuracy?

Example, in this case, with 72-YO eyes, a 9-inch seven-round group at 300 yards, with off-the-shelf ammo and iron sights.

Put a scope on it I am sure you well see the group size shrink.

quote:

Originally posted by p dog shooter:
Put a scope on it I am sure you well see the group size shrink.

Thank you. A very cogent suggestion.
Or, another way to shrink group size would be to stand closer to the target!