I would go with a 375 H&H in a Winchester Model 70 (new) or other makes second hand. If you really want a 416, I would get a 416 rigby- second hand. Otherwise, as you already have a 45-70 , you may want a 458 win mag or Lott.
My brother and I have CZ 550 in a 416 Rigby (him) and 458 win...