Not .308 experience, but have to hunt with non-lead here in California, so you may find some relevance. I use the Barnes 130's in my .270 - pushed about 3100. I have taken several black-tail deer and some hogs here. One-shot kills. Devastating wound channel. I've yet to recover a bullet. Nothing has moved beyond a foot or two.

That being said, I've always believed bullet placement is more important than the bullet and caliber. If I didn't want them to move, I'd look at a high-shoulder shot to at least immobilize the front end, and (if my experience with Barnes is any indication) disrupt the spinal column so that they dropped on the spot.

Hope you find your solution.