You are in "a can of worms."
So you have a cheap to free barrel in .30. O.K. Threaded for a Mauser? Military Mauser? Mark X is the same. Mausers were designed around cartridges approx. 57 mm long. 8x57, 7x57, 6.5x55, 7.65x53. Etc. I think if you look hard you will find the Weatherby case is way too long for that action AND magazine --you want a single shot. Not to mention, a whole lot bigger around. Even the '06 is 63mm and a bit long. Doable, but not great with longest, heaviest bullets. So if you are thinking of rebarrelling a surplus military... not a great idea.
The .30/378 was designed for 1,000 yard target shooting. Burns a lot of powder. Expensive. Barrel life limited. If this is what you want... You might find a "magnum Mauser" action that will fit these barrels and this case. Expensive. As suggested, other magnums have similar range and enough power for north America. .264. 7 Rem Mag. In .30? .300 Winchester Mag. Tight fit, but doable.
As suggested, the .30/'06 is the North American standard. 1903 to 1950s as service rifle with surplus rifles and ammo and virtually free brass helps popularity a lot. Mr. Ackley improved it and did not recommend the improved version except with heaviest bullets. Mr. Gibbs blew the shoulder forward and got alot more. When the brass was common and cheap, this was great. Today when you buy brass?
.308 Norma [.30/.338 Winchester wildcat is almost identical] is another with great rep that should fit in a military action. Should. Takes work and time and skill. Belted case. You have to open the bolt face. Sounds to me like you have some homework to do and deciding. Your bucks. Luck.