I'll say if it is stress in the barrel.... it would continue moving on you. Not just the first shot in every group.I think if its a stress relief issue, the barrel would continue to walk as it heats up, rather than just settle after one shot.
However I'm not an expert on this, but I'll tag one in @Frank Green
I haven't read the whole thread but more questions than answers right now.
Why are the ES varying so much?
Cleaning?
How is the barrel fouling?
If I caught it right... 800 rounds on a 243win.? Also could be at the end of the barrels life and it's being erratic.
If we do any testing at times... guess what caliber we pick to do it in usually? Yep 243win. because it so hard on barrels.
A 243win smokes a p&v test barrel in about 800-1000 rounds. Usually don't get much more than that out of them.
How does it shoot at long range? 500 yards or further. If the groups overall are poor... pull the stick and put a new one on it. It might be shooting good at short range but if long range is poor.... that's telling you the barrels on it last legs and it's a warning sign.