If you can get a date on the rifle, Midwest Gun parts carries barrels for guns made from 67-92.

They do have .338 barrels for that model.

Having someone make a barrel could turn into a can of worms just because it isn't a platform that a lot of folks work on but having a factory barrel would be (more) cost effective.

If you convert it to something like the .358 Norma mag, you can get a rebore on a 7mm and the chamber should clean up correctly.
.416 would be epic but quite a bit more barrel work.

The only other advice would be to have the barrel cryo'd after the work. I have had good luck with that helping accuracy

Neat project. Good luck.

Tom