Don't sell the Mosin short. They (if you have a decent barrel) are quite accurate. 3-3.5 MOA isn't as bad as most seem to think.
Think about this, the X-10-9 ring on the NRA 600 yard target is about 18 inches across. A 3 MOA Mosin is capable of keeping all the shots inside the 9 ring, the law of averages means that about 2/3s of those shots should be in the X-10 rings. Meaning, the gun is capable of 195+ out of 200 possible.
The 200 yard NRA target used in CMP Games has a 3.5 MOA X-10 ring, you should be able to clean the target with just about any Mosin.
The shooter is the weak link.
You see a lot of sub min rifles and groups talked about on the internet but you see very few cleaned 600 yard targets on the firing line.
You take the time to learn to shoot the Mosin, you'll be supprised.
I would highly recommend anyone who wants to learn to shoot the Mosin take a CMP GSM Clinic. Then practice. Dry firing the Mosin goes a long way in learning to make it shoot, Make some dummy rounds and practice loading with stripper clips. Dry fire "rappid fire" working the bolt.
I put on a CMP GSM Clinic & Match last weekend. Out of the Vintage Rifles, the two highest scores were Mosins. (There were Garands, Carbines and 1917s on the line). Not saying the Mosin will out shoot a Garand, but the Mosin shooter outshot the Garand shooter.
Chances are your Mosin is going to shoot high. Most do, but that's a easy fix without replacing the sights, and keeping it "as issue". Do a search as I've covered it a few times or PM me and I'll give you the simple details.
To add: What I like best about the Mosin rifle is it allows everyone to get into competitive rifle shooting, keeping shooting sports from being a rich man's support. To be competitive in High Power Rifle shooting, the rifle is going to cost about a grand, (three times that if you go to a M1A) plus the expensive ammo, heavy coats, etc etc. With the advent of the CMP GSM Vintage Military Rifle games, just about anyone can be competitive. You can use a $100 rifle and cheap surplus ammo (that normaly cost less then reloads) and can clean the target if the shooter learns the rifle).
Enjoy your rifle, keep it "AS ISSUED" and learn to shoot it. It will last you a life time.