NitroSteel,
There is not much to choose from for us Lefty's in the big calibres . I use the following-
Winchester, 70, "Classic Safari Express" .375H&H and have had no problems with it .
Winchester, 1895, .405Win. This rifle ejects straight up so suits left or right hand.
But for a .416 Rigby you might have to get a Custom magnum mauser action from Wells in USA or Dumoulin in Belgium both expensive but top quality.
RLI