I also have an American 308. I just use the Past pads.
Would also consider:
Changing butt pad to a Decelerator or Limbsaver
A slip on pad
A recoil reducer in the butt (although I'm not sure that is an option in the synthetic American)
I have a brake on my 300WSM and it does cut back the recoil. However, it would also blow out the ears of anyone beside me. I'm careful of my shooting buddies.