When you a 416 RM barrel, are you referring to something like Blaser R8 with interchangeable barrels?
I have a 416 RM Winchester model 70 SE. I've only shot one Cape buffalo with it, using 400gr Swift A frame bullets, but it did a fine job. I've also shot 3 Australian Water buffalo with a 375 H&H with 300gr TSX bullets. To be honest, the 375 did just as well as the 416 with similar shot placement. Maybe Cape buffalo are tougher than Water buffalo, not sure, but they have similar body weights.
As for Elephant, from what I've read, the 416 is definitely the right direction to go, even though the 375 would do the trick in most situations.