Bowhunter,
Per Bart's suggestions, keep in mind military barrels frequently have war-time tolerances. If you look at a blueprint for the M1 Garand, for example, it is 0.308±0.0015 inches, so 3.065"-3.095". If your M39 has a 0.311" nominal groove diameter, you have to allow that it could actually be off a thousandth or so (I don't know what tolerance in Finns specified).
My first search came up with
a post on another board suggesting the Finnish Mosin Nagents have typical 0.3095" grooves, and that it was the Russian and Polish versions that were nominally 0.311" but often much bigger.
The Bolt Man at the Russian-Mosin-Nagent-Forum.com said:
I have Russian and Polish examples with groove diameters running from .313” to .315”.
The only information I have been able to find that lists Mosin Nagant groove diameters indicates Russian groove diameters at .311” and typical Finnish groove diameters at .3095”.
So slugging is maybe the only way to discern what diameter range you actually need to be in. If you haven't slugged a bore before and you don't have pure lead bullets or sinkers or round balls a little over, Meister Bullets offers slugging kits. You would want
the #4 kit which is for 0.308" through 0.327" groove diameters and will do five barrels in each of the 9 slug sizes they provide, so you can mess up a bit as part of the learning curve. The instructions are detailed. I would strongly recommend you measure using a 1" O.D. thimble micrometer with 0.0001" resolution either
on a readout or
on a Vernier scale. A dial caliper will let you see between thousandths if you have a pin gauge to calibrate it with, but it takes more skill to use accurately without deflecting the jaws or the beam any.