Your rifle is grouping poorly because of odd barrel vibrations at that bullet weight and speed. And also because the bullet is OVERstabilized. Over stabilized? Yup.
Your barrel has a twist rate designed for 180-gr bullets at 3000 fps or so. That spin rate is way too fast for a 125 at 3400 or so. Several things happen with too fast a spin. One, the bullet can be so stressed from internal forces (centrifugal effect) that the jacket can actually bulge or even rupture after it clears the barrel. Second, because it is over-stabilized, the bullet can hold a position that's not perfectly in line with the airflow. If it flies "cocked" off a bit, it will tend to fly in that direction, rather than straight. No two will fly the same, hence the large group.
It's also difficult to get a powder that works well with that combo. Either the burn rate is right but the load density is low, or the density is good, but the powder is too slow. Low load density (partly empty case) can contribute to erratic ignition and burn with some powders. On the other hand, a light bullet won't produce the correct resistance to a slow powder that ignites and burns properly with heavy bullets. Neither combo is good.