Yes, that's going to be very interesting to see what components I was able to gather up for the gun's cartridge feed, and then how the .416 Rem Mag wants to behave upon being directed toward the feed ramp and into the chamber
As you already know, both the .375 H&H Mag and the .416 Rem Mag have a belted cartridge with the same base diameter and overall length, and therefore only leaves the slight difference of how each casing tappers up to where the bottle neck starts.
Finding .375 HH magazines, springs, followers is difficult enough but the .416 components are like hen's teeth, and so I have been doing screen captures of all the 375 magazine parts that I can find.
Will even look into if the .375 HH follower can be machined to provide better alignment for the 416 cartridge.
I chose the Nosler .375H&H 300gr Accubond white tips for my Remington721 rifle, and the Barnes 400gr TSX for what will be the Savage .416 Rem Mag rifle
I seen LOTS of those blunt round-nose bullets on online shops, and I certainly know they will do the job on whatever they come intact with, but I like the aggressive looks of the bullets that come to more of a point and so that's what I went with ... as I had previously said, I'm not using either big bore rifle for big game but they're simply to enjoy having fun and making noise in the neighborhood.
The following pics are just for some visual comparisons/references:
The bigger problem is the recoil forces and their consequences. You'll want to step up to a premium bottom metal rather than the garbage cast pot metal options. I believe once upon a time Savage did make a one piece bottom metal for some rifle that had the same bolt pattern. Custom inletting of a stock, glass, pillar, and bushings all would be required obviously. Foggy memory suggests either the safety or the bolt release became a problem, you have to move one of them, I believe the bolt release from trigger to left side or vice versa.
Whatever it takes with custom bottom metal to get you the rigidity you'll need is what it has to be. And of course you need to get rid of the unreliable external magazine both for rigidity and also so you can machine a custom follower internal to the gun to get the reliable feed for a 416 Rem.
It's a really hard job and you're going to learn a tremendous amount through the process. I would have started with a Mauser or a pre-64 winchester to save hundreds of hours/dollars on the project myself, but that's looking back in arrears and not looking forward to the steps ahead.
Savages have a tremendous amount of space taken up in the action outline for safety, magazine, and bolt releases. A custom, overbuilt stock will help you tremendously when you realize how little room you'll have to work and how insufficient the stock will be for recoil forces even if glassed, pillared, bushinged, and with custom one-piece bottom metal.
The Sav-1 Riflebasix trigger does struggle with recoil. On calibers producing about half your potential recoil, I was able to keep them together by setting them at 3.5lbs or greater and using blue loctite. Make sure to check often, you may need to use red or green loctite instead, then use stones to customize the trigger creep and pull, OR just make a CNC of one oversized and hardened, then use stones to customize the trigger without movable fasteners that are not trustworthy in a big gun.