This is probably too late for an old thread, but here are my two shillings:
For a large inexpensive rifle in 416 the simplest answer is to handload the 416 Rigby.
For the 416, if I wanted 400 grains at 2400 fps, then I would get a 416 Ruger or 416 Remington. The same calibres would run the 350 grain .416" bullets at 2600 fps. However, if someone has a Rigby in a modern bolt action like the CZ, then loads that are probably in the high 50's and nudging 60,000 psi are very doable. Study the following picture:
These Rigby cases are from a 2013 cape buffalo, as is the bullet. The primers are delightfully rounded and are not pushing true max loads or flattened primers. Think of these loads as conservative, restricted loads for a "416 Weatherby-ish capacity."
The load? 101.5 grains Reloder 17, Fed 215 match primers, Hornady brass, and 350 grain TTSX bullets for an adjusted, chronographed muzzle velocity of 2825 fps.
The Rigby is basically equivalent to the 416 Weatherby, with 3-4 grains less powder and zero freebore.