Most of the problems are with the varying groove depts and bore diameters. A .310" will work 'good enough' in most mosins, but if the rifle happends to have a groove diameter greater than that, and likely will, its hard to get good accuracy with an undersized bullet.
If you carefully fit a cast lead bullet to the barrel of the rifle and slow it down to around 1600 fps, shooting MOA shouldn't be too difficult, not only do you have a bullet that is of the right size for the bore and grooves, but you are eliminating much of the violent vibration caused by full power loads.