Shin,
I may be wrong, but isn't the .375 Winchester a rimmed cartridge? If so, then it isn't going to feed through the mauser without extreme feeding problems, which may never be cured. Remember, gunsmiths charge by the hour. Sometimes, even experienced mauser gunsmiths have to tinker with the feeding issue for 2 hours or so, and still not be able to give you 100% reliable feeding.
The absolute worse thing you can ever do is spend all of the time and money setting up a mauser 98, and then end up with a rifle that jams. Do yourself a favor, and forget the .375 idea. You will just be buying a big problem.
Go with the .257 Roberts. I think that if you check with Midway, and Brownells, they may have threaded and chambered 98 Mauser barrel, in .257 , that are ready to go, at reasonable prices.
One thing to consider though, is that you are going to end up with a pretty darned heavy rifle, in such a mild cartridge. You may be alot happier if you go with the .25-06. It is a long action round, that will feed smoother than the .257.
Just my experiences. (Once spent almost $2,000 plus a year of time setting up my "Dream 98 Mauser", only to have it jam occasionally, and with a chamber that was too tight.)
Mannyrock