With your .416, you chose wisely, right in the middle!Interesting video. Especially the vintage clips! My thoughts….Neither raw kinetic energy nor precise placement are the complete solution to routinely and humanely killing large animals. It takes some of both. If cartridges were on a spectrum with the 700 NE on one end and the 7mm Mauser on the other, I reckon that the ideal DG cartridges are somewhere in the middle. I like my 416s for DG. My 458 Lott is at the top end of my recoil tolerance. I don’t own a double yet, but when I buy one it’ll be a 450/400 or 470.
I’d suggest going with the .470 if DG and elephant are on the menu. Given that you’re already comfortable with a .458, recoil shouldn’t be a major concern. And there are some rather sexy powders, like RL-15, that can make it relatively straightforward to find the right velocity and accuracy.

I’m not kidding, Sir. You might even have been thrown into the fire for good measure! 