Firebat, go for the .308 barrel.
It will be cheaper than a special order .310 barrel and you might actually get it this year.
I have a 1942 date, 91/30 with a .3085 Soviet factory bore. To bad it's a refurbed mixmaster but the darn thing shoots both bullet diameters very well, even with my aging eyes and iron sights.
Thankfully, I don't believe the rifle was issued after the FTR.
I hand load and shoot factory ammo through it, both surplus and Privi.
I would also go for a different cartridge, like the 303 British, simply because it will fit in the magazine well and feed reliably. Easier to find a gunsmith with a reamer as well.
I would also get it drilled and tapped for a scope mount of a type that suits your build and will accept a modern scope, unless you're trying to keep it period correct.
I like Mosins, especially accurate Mosins. Some of them shoot far better than the capabilities of their shooters.
I think you're getting into an interesting project
There aren't any pressure signs at all, with any of the factory rounds or my handloads which were loaded with 165 grain boat tail hollow points to around 2750 fps.
I tried faster loads but 2750 was where it shot best.
Your call, if you have lots of good brass for reloading 7.62x54R and can find a smith with a reamer, go for it. If you have to buy a reamer, add a couple of hundred to the build.