I have done it, more than once.
It's not really hard, just a bit of careful work. Remember, most of these were built in a screaming rush and the "little" things (trigger, general fit, bedding etc) tended to be pretty crude. OTOH, barrels were generally quite decent, so you HAVE something to work with.
Check your Barrel first. Is the muzzle worn? Is the muzzle beaten-about badly enough to interfere with a bullet passing from it? If the answer is "yes" then a recrowning is necessary. If the damage is deep, as from poor cleaning, then a counterboring will be needed. If there is nothing wrong with it, LEAVE IT ALONE. The Russians always did make p*ss-poor stock finish..... but they always made good barrels. Don't get the two confused.
Handloads: an absolute MUST for decent shooting with ANY military rifle. Commercial ammunition is sloppy enough, but guys today are buying, paying good money for, ammo which is "surplus" to Russian military needs (meaning that it no longer passes inspection); they are paying good dollars for Ivan's 50-year-old scrap. If you have a supply of surplus ammo, treat it as components or bore-warmers or such, but do not attempt to rely on it for accuracy. LOAD with fresh Boxer-primed brass, an IMR-type powder...... and a .312" bullet. YES, I hear it now: "The Russians load it with a .3105" bullet!" To which I reply, "So what? It SHOOTS better with a .312!"
The Rifle is the Boss. IT will tell you what it wants.... and the Moisin-Nagant rifle wants a .312" bullet. Specifically, it wants that .312" bullet seated OUT just a bit and with the velocity just a bit under military. With the Hornady 150, this means seated so the whole cannelure shows. Generally, seating commercial bullets to the OAL of a Ball round will crowd the rifling just a bit. This is good because most military rifles are throated a bit deep, anyway. Lowering the muzzle velocity a bit lowers the chamber pressure a fair bit, meaning less stress and strain on the rifle for each round. I don't know of ANY machine which runs its very best flat-out, all the time, and a Rifle is no different. I lower my .303s by about 200 ft/sec and I get excellent results. The 7.62x54R is just a .303 with a Russian accent: the original factory was tooled by Greenwood and Bately, one of the original contractors for the .303! Lower your MVs about 10% and watch the groups tighten up.
Triggers: the MN is notorious for having absolutely the WORST trigger of any military rifle. Partly, this stems from the original design for the thing, which is ingenious and uses 2 SIMPLE parts rather than 4 or 5 COMPLEX parts. Mostly, though it came from wartime production standards. "Bozhemoy! Is go-it BANG! Send to Front, Tovarishch! Need lot more, duzhi sorok!" Perhaps we shouldn't joke about it; they were building these things to SURVIVE, not to shoot Olympic scores.
Take a careful look at the NOSE of your Cocking-piece. Is it pitted? Is it rusted? Does it have marks from WEARING against the SEAR? If you answer "Yes" to any of these, it needs to be stoned.
NOW look at the SEAR where it holds the Cocking-piece back. Is IT smooth? If not, it should be. Carefully check the ENGAGEMENT of the Cocking-piece and Sear. That CAM surface on the Trigger is there to give you a crisp double-pull letoff rather than the horrid, scraping, grinding, gritty feel you normally get with an MN. Clean up the CAM until it gets that way, then polish the Sear surface and the Cocking-piece both until both pulls are SMOOTH. Check the height of the Sear; if it is too high, stone it until you get a CRISP letoff with hardly any motion from your second pressure. I you cant figure out what I mean, study the triggers of Mauser AND Lee-Enfields; the MN trigger is mainly Mauser but TUNES more like an LE.
Bedding: a lot of guys will curse me for this, but you said you wanted an ACCURATE rifle. Bedding on these (as on LEs, Mausers, etc) was by hand only but, if they had had modern epoxy bedding compounds, I am certain that they would have used them. The Canadian Forces of today approve epoxy compounds when setting up competition rifles, so why not use the stuff? I do NOT use the epoxy the way it is instructed in the kits; I use as little as POSSIBLE and generally I get at LEAST 4 rifles out of a kit, generally 6. The guys (and girls) who BUILT these rifles knew what they were doing; they just were in one awful rush. And the rifles themselves now have had 67 OR MORE years for that hastily kiln-dried wood to work its kinks out. So you simply use the epoxy compound to RESTORE the original bedding job to what it SHOULD BE.
I use Acra-Glass for my bedding jobs and it works fine. I do NOT hog the wood out of the stock; instead, I dry the wood surface from any Oil or Grease beforehand. I GREASE the action with the THINNEST coat of Grease POSSIBLE: just enough so that the wood and the iron are not glued together. I use a pretty BLUE grease for this, ESSO UNITOL, which you can see readily when it comes time to clean it out. Then I mix the bedding compound and place it into the stock, using the thinnest bed that I can get away with and still seat the entire action into the stuff. You bed the ACTION and CHAMBER SOLID, then NOTHING ahead of that, then put the rifle together carefully and let it sit HORIZONTALLY, in firing position, for 12 hours, then take it apart and clean up the excess Acra-Glass with an eXacto-Knife, then put it back together and let it cure another 24 hours.
Pull it apart and FLOAT the barrel ahead of the Chamber: NO contact, all the way down the barrel, except that a really good idea is a 2-inch contact section at the extreme forward tip of the Forestock. If this section needs to be built up with epoxy, do it, but remember that the barrel is NOT supposed to touch the upper handguard.
Your rifle NOW should be good enough to test.
I have done this to a couple of MNs of wartime manufacture and was nicely surprised when the things started shooting just a bit over 1 MOA with the factory sights, and handloads, off the sandbags. It CAN be done.
When shooting off sandbags, BTW, be sure that the FULL forward section of the stock is on the bags, NOT the really thin forward section, which is just there so you don't burn your hands. This is VERY important to best accuracy.
So that's how I do it...... and it works.
I will run away now. There is sure to be someone come on shortly and tell me I'm full of sh*t, but this works fine for me, anyway.
You DID say that you wanted ACCURATE.
Hope this helps.
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