The barrel jumping left to me says you need to shift where you place the stock in your shoulder. We always say shoulder, but in today's long range shooting it should be more on the pectoralis.
As many here talk about natural point of aim, that's how I learned to shoot. But, as that was old style, the feet were off slightly to the left, (I'm R. handed) and the rifle pointed slightly left across the body.
What I learned here on SH was to put your feet equilaterally straight back, move the butt inward and the rifle points straight forward. Traction is with the balls of the feet. So, get the fee flat. The reason for this is at long range small changes in velocity affect poi height. Flexing with the shot while the butt was in the shoulder pocket, and slightly crossing, doesn't give consistent movement rearward, which translates into different velocities. The minimal change in velocity doesn't mean much where we all used to shoot out to 500 yds. But at 1k+ is where that larger deviation starts to really show.
IME, completely stopping the recoil works best for long range shooting. WB300 I gotta say I like the sandbag analogy. Too often I too get too tense and even if the rifle doesn't go off in a different direction, it goes forward and adjustment is needed to get back in position for the next shot. But, when the recoil is totally stopped and I don't have to shift is when I do a lot better. You can really tell when you are on when you can watch the bullets hit. I'm not talking seeing where the dust kicks up after the shot. I mean watching the whole process and being able to actually see the hole get punched in paper or the splat on steel.
As mentioned above, one of the difficulties of the "straight back" style is that elevation of the rifle and the head relationship is harder to attain. Dry firing helps a ton. When you get on the range, get prone and practice your position a lot before starting firing and I'll think you'll find when you get comfortable in it, it helps.
