I shot a .577 double. Once. After a while I commented to folks that if an elephant was charging me, and the rifle was laying in front of me, I'd have to think about it...
I've shot my .475 Turnbull & .458 off the bench - both with 500gr full-house loads - and it was not fun, but not horrible. The .475 only weighs about 9lbs, 2oz with scope. I think my recoil limit is somewhere between .475 & .577
You can get 350gr TTSX for a .416; I think those would have to be fine for anything except elephant.
