I got some good information for you as I own a 1943 91/30 and reload.
There are a number of things that can be done to improve the accuracy of a Mosin Nagant
When I first bought my Mosin, I got some surplus Bulgerian ammo and some Highland commercial ammo. Accuracy at 50m was non-existent and I honestly thought I had wasted my money. It was approximately the size of a large dinner plate at 50m. After doing a lot of reading and research into bettering the accuracy of this rifle, my first step was to check the bore condition (which was excellent in my case) and slug it.
The reason mosin nagant owners should slug the barrel is because the general bore size of these rifles vary between .3105 to .315. Shooting projectiles that don't fit the bore size can lead to inaccuracy. Get yourself a lead sinker that is slightly oversize to your bore and from the muzzle end, tap it down the bore. You'll need to get some wooden dowel to help push it through the entire length of the barrel and out of the action.
Once you recover the lead slug, measure the outside diameter and that size will be the projectile diameter you'll need to shoot. My 91/30 slugged a .314 bore and I have shot .312 and .311 projectiles with better accuracy.
Secondly - Check your muzzle. My muzzle was well worn from a cleaning rod and I needed to remove about 1/2 inch of the muzzle until I got good rifling the entire length with a clean crown. I sent my Mosin to a gunsmith for this fix. Since I was keeping the front sights, I was lucky I didn't need to remove more than I needed.
Take the rifle to the range again and test accuracy for any improvement using commercial rounds. For me, I had little gain, but any gain is a good gain.
My next step was looking at Free-Floating the barrel since the mosin has a very long, thin barrel, which is more susceptible to barrel harmonics. I took the action out of the stock and began to sand back the barrel channel until I could slide a business card all the way to the receiver. Most people will use paper for this test but I wanted something a little thicker for my own preference.
During my reseach in accurizing the Mosin Nagant, the book called "Sport Shooting" by A.A Jurijev was commonly brought up in other forums because there are very helpful tips and modifications that help trigger pull and bedding. The illistrations in the book (although all text is Russian) show roughly where the important nodes are barrel bedding tips.
Another simple tip for accuracy is to add cork. Visit this website
http://www.theboxotruth.com/docs/edu63.htmI have done this and noticed increased accuracy yet again. For a 50m target, my groups went from a dinner plate to about 3-5 inch groups. Although at this stage, I should note I had already been handloading custom rounds with a Hornady 174gr Round Nose pill with 2209 powder.
After more range testing, I had found a recipe of 47gr of AR2209 and Hornady 147gr Spitzer .312 pills showing much improvement and groups shrank down again to 2inch at 50m. Accuracy out to 100m was about 3 to 5inch on average.
Sticking with this load as a default load for all testing and hunting, I decided to start looking at my trigger because the length of pull and weight of pull was a little too much for my liking. A greater weight and trigger travel can pull the Point of Aim to the side just as your pulling the trigger, which also results in inaccuracy. Taking the advice from the "Sports Shooting" book from A.A. Jurijev, I took apart my trigger assembly and began to add a very small bend in the sear spring. This lowers the sear to release the firing pin for a more crisp release. I also added a trigger return spring to remove the slack in the trigger.
*The above modification is highly dangerous and must take every precaution to check your firearm for absolute safety. Modifying your trigger mechanism to adjust your sear engagement can cause the firing pin to be released under a small bump. Please get a gunsmith to do this for you if you are not competent to do this yourself, otherwise leave the trigger alone*
In case you hadn't noticed yet, I wanted to keep my mosin in the most original way possible so the modifications I've done were kept to the WW2 era.
All this work to get my rifle shooting its best was all coming together and now my rifle has a lighter trigger pull, was able to place groups at 100m 3-4inchs. Increasingly getting better with any small changes to handloads.
My case preparation involved keeping the same case manufactures in the same string of shots, I only resize the necks using the Hornady 7.62x54r neck sizer die with the .310 (I think) neck sizer ball, Cases were trimmed to correct length, all cases deburred, each round was seated at exactly 3.000 inch for Cartridge overall Length and CCI LR200 primers.
Mosin nagant rifles love long projectiles. Since I was using a 147gr Spitzer, I thought I would try the Sierra 180gr Pro-Hunters projectiles and at my last range session, proved to be a real winner. I tested five different powder charges ranging from 50.5gr to 52.5gr of AR2209 powder. I was amazed that now my 91/30 with plain iron sights can shoot sub MOA if I do my part.
This is one of the targets at 100m. There is two groups in this picture. The first group was a group of 4 shots that is very tightly clustered together next to the number 5. The 4th shot went though an existing hole. The 5 shot vertical string is a little weird but I think that was me due to just finishing lunch with a greasy grip and a little exited.