If I were going to do this (and I cant say as I would) I would try to find a Model 70 in 300 rum and rebarrel it. The mag is already set up for the Rum cartridge and should be an easy fit. The best part of these is that they are cheep (as the RUM cartridge is useless IMHO), CRF, and you should be able to pick one up for under $500 as a complete rifle.
For what it is worth why would you want a 375 RUM. The H&H is all you really need in that caliber and if you need more go bigger diameter (ie 416, 458, 475 etc) :grin: