I had a Mosin that turned out to have a cracked stock. I used it as a project to see what I could do to the stock to improve accuracy.
Starting out with the cracked stock I was getting groups of 6-8 inches at 100 yds with Brown Bear 203gr hunting ammo.
I put epoxy in teh crack and ran brass screws through the stock to close the crack. I then used JB weld to make bedding areas for the action, where the action screws come through the stock to hold the action in place, as well as at the recoil lug area. This was to give better support to the action, and prevent teh action from slamming into the recoil lug and cracking the stock more/again. (I could give more detail on teh process, but you can look up bedding arifle action. Use some paste wax or other release agent before bedding the action, so that you do not glue it into the stock. It should be a skin tight fit, but not glued in.
After bedding, I then screwed the action back into the stock. With the handguard off, you can take a dollar bill and run it in the barrel channel under the barrel, by feedint the bill halfway and wrapping it up around teh barrel. Then slide the bill from front to back noting with a pencil any spots where the bill drags in the barrel channel. You should be able to get the bill up near the rear sight or just behind it. If you have a good socket set with deep well sockets, like you would use for spark plugs, you can find one that fits the barrel channel pretty well and wrap some sandpaper around the socket and sand the areas that you marked in pencil. Remount the barreled action in the stock and check again until you can move the dollar bill along the barrel without it snagging or dragging on the stock. The big thing with a Mosin is just to get all of the irregular pressure points of the barrel at random places.
I did this, and my groups went down to 3" at 100 yds, with some vertical stringing. Someone had told me that some Mosins like to have a little upward pressure near the tip of the stock. So I had taken some card stock (index cards) to the range. I slid a piece of index card in the barrel channelat the last 2 inches from the muzzle end of the stock. Groups were about the same. Another thickness of index card, and the groups came down to 1.75". I tried a third layer and group size went back up to 2.5".
I then found some cork gasket material and put it in the barrel chanel after I got home, and groups have settled in arounf that 1.5" (with some Russian Match anmmo) and 2.5" With some other surplus stuff that has bullets that mic a little smaller than the loads the rifle really seems to like, which isn't bad for a rifle that started out shooting really random patterns with anything.
So the things I learned are:
Some Mosins may like to be freefloated, while others may need some upward forend pressure to keep barrel vibrations more consistant.
Ammo makes a big difference. I found that my barrel likes bullet diameters that are closer to .312 than .310.
be prepared to experiment a bit. Not all of these rifles will respond the same way.
Good luck with your project.