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Before you drop a bunch of money gunsmithing your rifle,consider spending the money on a basic,lo=buck reloading package.Lee might be your friend here.You need a scale,a couple of manuals,some dies and a press.A powder measure is a good thing.The $200 you propose for a barrel will fix you up.
You will be able to learn what ammo your rifle likes,and you can make match grade ammo.
This will accomplish at least 3 things.
You will eliminate poor ammo as a variable
You will have more ammo to shoot,so you will shoot more
While it is possible,if you alter your rifle,you might improve it,from the start,as the crufflers will emphaically tell you,it is no longer a pristine K-31.The first thing someone who appreciates the K-31 is going to notice,is someone "bubba'd" a nice rifle.(I do not know the K-31.I do have an idea who the Swiss are)
It seems possible you may act before determining the root cause of a problem.The rifle gets compromised,it does not improve,it may get worse,and you lose the money you spent.
Do a search on all the posts of kraigwy.Read them.Read what he suggests you read.Another decent book is "PositionRifle Shooting"
Once you develop as good a load as you can for your rifle,go ahead and shoot your best bench group with the rifle,and sight it in.Save the targets.
Then get off the bench and shoot position.As long as your position shooting groups significantly larger than your bench groups,the best way to make your rifle shoot better is to be able to shoot as well as your rifle does.
It may be that the other path leaves you frustrated,broke,with a butched up basket case gun .Or you could be shooting.
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