Can it be that the rounds are not chambering the same when the bolt is released on the first round, compared to the action slamming the bolt both ways on subsequent shots?
That is what I've seen Chad explain is the case. I learned from him, doing load development to load two extra rounds. Throw out shot 1, shoot three to five, and leave one extra round in the Mag to be chambered but not fired. That is so the bolt does not lock open on the last shot in the group.
I have observed this situation on my own LR-308. Shot #1 might be .2 Mil lower than the next shots. The key is to "know" what the rifle is going to do, and it looks like you know. So you can adapt to it, and hit what you want to hit.