Lighten the knock-down targets? Very odd. 7.62x51 has the same ballistics as .30 M2. I don't remember knock-down targets in that time frame. We used the old 5-V bull. Perhaps an urban legend....................
.308 should be perfectly adequate for black bear. 180 Noslers will be fine. I don't like the 180s so much in the .308 because of the low achievable velocities vs. the .30-06, but at woods ranges there should be no problem. Calculate the trajectory and zero at 150 or 200 yards.
Take your time and put the bullet in the right place.