I would suggest a couple of things

1. Try fire lapping the bore - roll .311 lead bullets in 80 & 120 grinding grit & reload with a gas check & fire at say 2000fps - 10 shots each. Then slug the bore & see if it is .312 or more. Then shoot normal bullets & see how it groups. This will not cost you much & could make it into a serviceable rifle if the pitting is not too deep & if the barrel crown is ok.
2. If this does not shoot well, then I would re-bore it to a 8X57R with .323 bore. I feel that .375 is too big for that barrel - I have a 9,5X57MS & the metal around the bore looks as thick as this. You are looking at 0.032 inch to be removed from the wall of the bore to make it 0.064 larger in diameter.

I would also have the crown re-ground before I try re-boring.

Good luck rifle.