I'm in agreement that .338 should be the littlest round that you look at, I'd say either go wildcat, .375 H&H .416 rigby, or .50 bmg. I've seen a .50 bmg perform on deer at a mile, and it did more than well enough on the accuracy and power. Only thing I'm curious about is, why take a 500 yard shot? Look at any projected trajectory chart, and even the flattest shooting rounds are falling around five feet at those ranges!! Once they pass 300 yards, the bigger boys are falling fast, and the .338 has lost most of what made it great, speed that is, so it's falling pretty fast itself. Don't even look at the .300 win mag, it's not that much better than the .30-06, and no .30-06 should be going after a bear at over a quarter mile.

My advice isn't the round, it's the hunt, get closer.

Screw the 10 ring, keep them in the zero!!!