I'm going to be about $7,000 in to my 338 RUM. Including optics (low budget for ELR) 338 RUM specific reloading gear, rests and a case.
I could have shaved maybe $2,000 off of that if I went absolutely entry level or built off a Savage.
Stepping up to a 338 Lapua Magnum would cost more because for safety margin you have to go up to a larger barrel shank. Stepping up to a big .375 is even more because you are 100% stepping outside of the Remington 700 compatible platform, everything is going to be specific to a big boomer.
Reloading for a big boy is very expensive too, if you are trying to shoot 1 mile+, you're probably going to need fancy lathe turned bullets which are a lot more than a lead core jacketed bullet. Even 338 has a premium, you would think that bullet price would scale with mass because the labor shouldn't change much between. A .223 and a .50 but the jump in cost from .308 to .338 bullets does not scale.