Paparock, sounds like you know exactly what you want. I don't know anything about the .375 Ruger cartridge, but you've got the std magnum bolt face and a std magnum length magazine. If the Ruger cartridge has the .535" case head and is not longer than the .300 Win Mag, it could be a go. It might have feeding problems if the case is larger in diameter than the Win Mag. Also, on a custom barrel you would want to see how much larger you could make the barrel shank (chamber area diameter) to maintain strength with a fatter case.
Anachronism is correct; The .338 Win Mag would be a direct rebarrel job, but if the .375 is in fact a fatter case, it may also be a higher pressure rated (SAAMI) cartridge, which in my opinion would be a major red flag, which added to the possibility of feeding problems on a dangerous game gun, would be a deal breaker.
Maybe someone who knows more will jump in. Sounds like a very interesting project.
Good luck, Tom
Texas State Rifle Association Life Member
NRA Endowment Life Member
A big fast bullet will beat a little fast bullet every time