Hey BB, I will just throw in another vote for the 458X2", you have several action options, Ruger short, Win short, Rem short magnum.............and brass is virtually free as any belted case can be cut off and used. There just is no downside to the 458X2", also using belted cases you know you're getting a strong positive headspacing case to start with. I built a 375-350 RM on a short Ruger action and it exceeded all my expectations, I would do the same in 416 or 458 and the outcome will be beyond what you may believe.
The other option I would seriously consider would be a 458 WSM, just buy any WSM rifle as a donor, change the barrel and go..........should feed flawlessly and require zero modifications to be 100% functional. Put an 18" barrel on and use the case to bore efficiency and I think you'd be surprised at what you'd end up with.