I've never seen a 30/06 "tumble" although any bullet will deflect or deform if it hits something, including brush. I won't shoot through brush unless it's literally right up against the animal. You might also want to check regs in your area. In some (like mine) .223s (5.56) are considered too small for big game and not allowed. As I'm sure you know, shot placement is everything and not wanting to wound and chase the animal shows a great ethical decision.