You can attempt to accurize
an MN, you may not succeed.
It was a relatively low quality mass produced rifle. It got worse as WWII hit. Essentially a crap shoot if its a good one or not or something in between.
You can play with it and get it to do its best but you are not going to improve a poor barrel, only time, work and testing will tell.
That said, there is no reason not to try and see where it goes, shooting the old guns is fun and a lot more interesting visceral appeal than the new spiffy stuff.
Its also fun to nail a nice tight group. Each to his own or like me, I split down the middle, I like shooting the old guns and I like to do some tack driving. No reason to be limited to one or the other.
As for the OPs test protocol, phew. I start at no more than 50 yds and sometimes 25 is better. Get it on target, move it out, fine tune it and then get it good at 100. If its tight enough and consistent enough then you can maybe move to 200 but might have to keep stepping it out.
My last scope sight in at 50 I was 8 inches high. At 300 I would have been 48 inches high. I was also 3 or 4 inches left, 24 inches at 300.