The 7 BR will be just fine - I used one for years in my standard rifle and never had problems with rams or any of the other animals. I used 120's on the first 3 and 168's on the rams.
I experienced less ram loss with the 7 BR than any other cartridge I have ever used, 243, 308, 7/08, 7 TCU, my feeling is that the 7 BR seems to give the bullet optimum energy on target (push, shove, energy or whatever you would like to call it).
The best part of it is that you will probably also pick up hits on the first 3 targets due to reduced recoil and the fact that you can concentrate more on your hold and less on whats going to happen to you when you pull the trigger.