The 416 Remington and 458 Lott have always been on my want to shoot list, along with the 416 and 460 Weatherby. 458 Lott may be an interesting option for you since you are already shooting the 375 H&H.

I've shot three rounds out of a 460 Weatherby once. Memorable experience is a good description. Fortunately we were shooting off hand using a tripod as stability. Expect it would have been a lot less enjoyable/tolerable if I was shooting it off a bench.