When you get a shift as you have described, quite often you'll find by loading between the 2 powder weights will bring the group into a more uniform pattern. So you're on the right track with your thinking.
In the picture of the vertical spread you have classic double grouping, even a bit of double grouping in the horizontal as well, which is usually a stock issue(bedding or loose king screws),or loose scope mounts. If you're %100 confident there's no issues with the rifle, altering the seating depth of the horizontal spread could shrink that down to an acceptable level as well.
Be interested to see the results.
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