I discussed your problem with a friend today...
And he came up with something I had not thought of. Since you reported that the boresighter showed the crosshairs had moved after 3-4 shots, and at the time we assumed the scope/bases were not moving, then the end of the barrel is.
He asked it perhaps, the barrel had taken a hard knock against someting in the past? Not enough to visibly bend it, but maybe enough to leave a small dent in the metal. The compressed metal in a dent, even one too small to have any effect on the bore of the barrel, could have an effect on how the barrel vibrates, and how it flexes as it heats up. It is possibly that since your first two shots go together, they generate enough heat in the barrel so that followup shots are "flung" to one side or the other as the barrel vibrates/flexes unevenly due to a dent. It could be very small, and still have an effect on your group sizes.
Anyway, this is one more thing to check out.
I see from your recent post you have found a stripped screw in the mounts. The mount may still seem "tight" to finger pressure, but under the sharp jolt of recoil, could be flexing, as it is no longer being held evenly tight by both screws.
Let us know how things turn out, and good luck.
and of course, you're welcome.