375 RUM sounds like fun with a 350 grainer but, if it were me, I might shy away from a 416 rem for a couple reasons. First being the 416 Rem Mag is pushing 400gr bullets at about 2400 fps along side with the 416 rigby and the like. I don't think you would really be taking advantage of a high BC bullet like the hornady 450gr BTHP with probably around 2200 fps. Second reason being Hornady's website says the .416 450 grain HPBT Match bullet is "temporarily suspended".... With the shortages of components at the moment I wouldn't put a lot of faith in that. Plus, I've never seen that bullet for sale in a store or online, have you?
If you're going to expect a single shot anyway, I would look for a Precision Target Action like the ones found on the Savage model 12 F/TR. You can buy the action only for about $550. Includes everything except the barrel and the stock. As far as barrel length and twist... I have no idea. You'll have to enlist the help of some others on here smarter than myself.
Hope this helps a little.
Blueoval56