T-bone said,"It needs to be a magnum action."
That's not quite accurate. The Browning M98 based Mausers and the Mark X Mausers chambered to the .375 H&H use standard 30-06 length actions althered so that the longer round will work. Metal is removed from the front and rear of he action and while some say it's a bad idea, I've never hard of of a Browning or Mark X fail because of the way the action was altered.
FRankly, if I anted a mauser based rifle in .375 H&H, I would first try and find one of the Brownings made in the 1960's an 70's using the modified FN Mauser actions. Second choice would be on on the Mark X action. Frankly, the Brownings are quite pricey, especially in the H&H cartridges but would still be a lot less than converting a milsurp mauser action into something nice. A Mark X would be a lot more reasonable in either the Alaskan or (damned if I can think of the name of the other model

offhand.) maybe it'll come to me. back around 1973, I had the Alaskan in .375 H&H and it was a darn accurate rifle. Sometimes I kick myself for ever selling it. They are pretty light weight for a round that powerful but recoil is tolerable. If I was wanting anoher .375 H&H, I believe the Mark X would be my first choice in either model and the Browning last, not because it's no good but due to the price. Browning doesn't make those any more and collectors have driven the price up.
Converting a milsurp Mauser would be very labor intensive. You have to open the magazine, alter the rails and bolt face, bend the bolt to clear a scope and that's not counting the new new barrel. A better action to work with would be a J.C. Higgins M50. It too is just a 30-06 length action but they're made by FN in Belgium. I have two custom rifles based on those Higgins M50s and they're both winners. The pont in using one of those is you'd mostly likely only have to do the barrel, open the bolt face and action to handle the round and alter the rails for proper feeding. All the work of cleaning up the action was done by FN so you would not have the labor involved for that part of the project.
On second thought, go with a Mark X and save youself a lot of cash.
For the .375 Ruger you'd stil have to do much labor on the action where with a commercial mauser, just the bolt face, rail alteration and the new barrel just might do the trick, but I have no experience with that round.
My current .375s are Ruger #1 in the H&H versrion and a tang safety Ruger M77 chambered to the .375 Taylor which is the .338 Win. mag. necked up to use .375 caliber bullets. It's also known as the .375 Chatfield-Taylor and .375x338 Mag. which is how my rifle is marked.The round will do everything the H&H does with less powder and amazingly apparently less recoil. My 9.5 pound Ruger #1 in .375 H&H kicks harder than the .375 Taylor in a 7.5 pound rilfe yet velocity is equal to the H&H as determined with a chronograph. Rifle is in a ramline synthetic stock with a Pachmeyr Decelerator pad whie the Ruger is strictly as it came from the factory with that skimp red joke they call a recoil pad.
I've built a few rifles over the years using milsurp mauser and I'm here to tell you, many hours of work go into making one of those into a reasonably decent looking rifle. My 1909 Argentine DWM Mauser ran a hair over three grand and becuse I've given my gunsmith a lot of work from friends that I've sent to him, I got a break. Rifle would probably have been about $1,500 more otherwise. Good work don't come cheap. I've just picked up the fourth mauser he's done for me and that was just a simple rebarrel and rebed. That was $800 and change but the work is impeccable.
Paul B.