I'm mentioning the below because you say you see this with other rifles too.
The Vertical could be heat related but but could be pulling back into your shoulder at the shot. The Left/right in the group looks like you might be Leaning into the stock in anticipation of the shot, sort of like a flinch. If you lean into the stock (Right handed shooter) it will push the butt right causing the shot to go left. Pay a lot of attention to follow through and watch where your crosshair is on target "After" the shot. If the crosshair is to the left it may show that at the shot your leaning into the butt some. At the same time if you add just a tad more down pressure (Such as pulling back into your shoulder) at the shot then the combination could cause you to get diagonal groups.
Unfortunately if I don't shoot a lot for a while I develop a habit of picking up my head a little, or basically sitting up, at the shot like I'm trying to See where my shot hit. This causes me to drop a shot lower and my crosshair always ends up lower on target. The more I shoot the more I can break that habit when I am paying attention.
Also pay attention to your Bench itself. Line up the rifle (Unloaded) on target and then without pulling a trigger just lean a tad with your body into the bench and see if it moved the crosshair.
We have a few all wood benches at our club that are not the most firm and if you lean into the bench, just like leaning into the butt stock you'll push shots to the left, stop leaning into the bench and shots go right.
Last thing that comes to mind is Parallax. Put the rifle in the rest, and best if you use a good rear rest too for this, line up on target and without moving the rifle just move your head a little left right and up and down. If the crosshair moves around then your scope has a little parallax in it. If it stays put when you move it don't.