This was J.Y. Young's answer. Over a couple of decades he hunted every legal species of North American big game animal, something over 30 species as I recall. I've got the book here at home. Quite an interesting read.
Young used a simple Remington 700 30-06, with handloaded 165 grain Nosler Partitions. He switched to the 200 gr Nosler Partitions for the huge Alaskan brown bear, and I believe for something else as well.
Don't think he attempted any 500 - 600 yard shots. He just went about going after the various species one at a time. Sometimes he had to make several hunts to tag something. From reading his book, he has no regrets about choosing the 30-06 and 165's for the vast majority of his hunting.
This pleased me - because I'd settled on that combo long before learning of J.Y. Young and his hunting.
Worth a thought. I don't think many of us can claim to have taken everything in North America.
Regards, Guy