I-too would go for a .416 Taylor. The easiest brass to use is .338 mag. brass, necking them up in one pass with the FL die button.
: .458 Brass could also be used, but necking down is harder sometimes, than necking up. With necking up, you won't have a thick-neck problem that will show itself, if you use, say, shortened 300 mag brass.(which is a possibility as well, especially if .338 brass is hard to find. In reality, any 2.5" or longer, belted magnum case can be used, if neck turned or reamed on those too thick for the neck area on the .416 chamber.
: For a bit more work, well worth it for an anomolous ctg.and if a bit of one-up-manship is desired, a .458 Alaskan is also a possibility. In this respect, a .416 Alaskan reamer could be used to make up a .416 Alsakan on the blown .348 case for a magnum bolt, 98 mauser. A small lathe is nice for turning down the .348 rims, into a slightly rebated-rim case with .458 Win Mag capacity + a few grs.
: Shown is the .450 Alaskan rimmed, for lever actions, and the .458 Alaskan for magnum bolt faces with rebated rim. The same reamer is used for both chambers. The .416 "Alaskan" reamer could be used to make the same case for .416 bullets. This also is a 2.1" ctg. that feeds very well and allows any bullet seating depth needed, up to 3.2"