you are being way to cautious.
you can SAFELY use just about any bullet you like from .308 to .312.+ Just avoid maximum charges and you will be absolutely fine. 150 grain flat base bullets (Speer, etc) made for .303 Enfields etc. are usually very accurate in Finnish Mosins.
Most FInns slug out around .3087 -.3090). That's of course why your getting blow-by with .308.
Have you not fired any Surplus 7.62X54r?? Do you think that would blow up in your rifle? The Finns were more than well aware of the likelihood the rifles would be shooting Commie 54R ammo (i.e. compared to 53R).
in my actual experience with 174 +/- weights in both
various .303s and in Nagants, specifically, the BT "Match" SIerras and the 174 BT FMJ Hornaday, the both have proven disappointing in accuracy (with no exceptions that I can recall). I suspect it could be the powder, etc, but for some reason, despite a good bit of trial and error, I have virtually given up on both bullets and heavier bullets in general. 150 grain seems to work best at least at reasonable ranges (not exceeding 220 yards).