I almost went down the road to make a brush gun from a Mosin, but eventually decided against it. It just didn't add up for me.
Increased accuracy could come from bedding the barrel and/or action, the cork trick, recrowning, trigger job, trying different ammo, maybe a new barrel if you can find one.
Most Mosins are 3-5MOA rifles out of the box which is good enough for hunting deer within 150 yards or so. A trigger job, solid mount, good scope, and the right ammo, you may could get that down to 1-2.5 MOA. The scout mounts that attach to the 11mm rail under the rear sight would be one way to go, but a good scout scope costs more. The DIY drill and tap mounts that screw into the receiver would be another fairly solid way to go, but you would probably want to take it to a smith. This would allow you to use a less expensive optic though.
Basically, I realized that I could build a hunting mosin, but I would spend less money and probably have better accuracy by getting a used 30-30 Marlin.
I'm not trying to dissuade you from tinkering with your gun at all. It's just that I didn't want the headache of trying to make a gun when used Marlins are all over the place that can do the same job for the same or less overall cost. If you want to turn your rifle into a scoped hunter, have at it. I'm sure it will be fun for you.