Re: Not exactly long range but.....
The 7.62X54R can be every bit as good as the 308Win. With the long orig barrel, max vel will be extracted from the cartridge. It is also very accurate. Check with the bore dimensions, you may even be able to use 308 bullets.
I load my using a Lee collet neck die (308 with a shim washer), 168gr Nosler J4, Win LR, and H380. My rifle is quite shot out but will hold 1.5MOA with open sights. If you rifle is in good shape or a Swedish variant, you could easily have a MOA or better shooter.
Many Eastern Block countries still use the Mosin as their sniper/tactical rifle so the platform, although old fashion, is still very useable.
Look in Shotgun news for any match ammo which should be starting to be more available. Or else, get a Lee manual and load up your own. Norma brass is available and you may even be able to find some ancient Rem stuff.
I would not modify the action beyong this cartridge. Nothing else will feed. Don't go over board with the pressures either. The trigger is a simple affair that is very easily tuned to a light crisp 2 to 1.5lbs.
If not for the worn and pitted barrel, I think my Mosin would be a great shooter. Going to try and find a Swed/Finnish variant in good condition. They would be effective to 1000m.
If mounting a scope, you have to look at the POSP scopes with the Dragunov reticles. They are designed for this rd out to 1200m.