Go with a 165-168 gr Barnes TTSX and there will be no worry about bullet performance. A 150 gr TTSX is ok, too. I have taken mule deer and elk with 150 gr Barnes out of a 7mm Weatherby and 168 Barnes TTSX out of a .300 Weatherby. Never had to track a one of them.
+1
We've been taking game with the TTSX since they came out and the MRX before that. Most animals have dropped straight down, none have gone more than a few steps. Confidence in them is high enough that I recommended a 130g @ 3045fps for Daughter #1 and her .308 Win. She will be using it for elk and antelope again this year. If she shoots an elk I doubt we'll recover the bullet as we haven't recovered one yet.
