I would add a few things to check on an H bedded rifle that has a noticeable left or right hand shift in the group relative to a simple bore sighted expected zero:
1) Bolt lug fit. If one lug is not bearing or is just bearing by a small amount, the rifle will throw shots in the opposite direction. So if the left hand lug is not bearing enough, the front sight will have to pushed over to the left in the front sight base to compensate. The fix is to adjust the opposite bolt lug bearing until the group moves back in line with the bore sight zero. This step should not be done until the following defects are checked for:
2) Is the barrel mounted so that the bore line is true to the action body? If the threads or action body threads are not true or the rear of the chamber is not bearing on the full 300 degrees(less the extractor cut), then the barrel will shoot off of the expected zero. I have never seen a problem with this, but I have only looked at the rear chamber seat on 6 rifles, which is not a large sample size
3) Is the bolt head square relative to the bore line (i.e. a true 90 degrees relative to the center line of the bore)? If the bolt head is not square to the barrel bore line the rifle will throw rounds off of the bore sight zero.
4) Is the chamber concentric with the bore and action body? If the chamber is canted relative to either then the effect will be identical to having uneven bearing of the recoil lugs. I have seen some bad chambers that seem to be the result of over tightening the barrel to get correct vertical alignment.
Quickest way to check the last three issues is to look at the cases. If you put a fired case in a upside down die that is level and using a ball loaded caliper on a test surface, rotate the case in the die and see if the case head shows any run out, i.e. one part of the rim is higher than the other side by a few thousandths if it does one of the three issues above is a problem. If there is no run out or less than .001, then the chamber, action threads are not an issue. Note to check the run out in a test set up, use a new case as a zero gauge
If there is noticeable run-out do not despair, all is not lost. The first thing you should do is to apply the old Ed Horton trick of putting a small ring or spacer around the cases at the bottom to ensure when the action is close that the round of ammunition is held against the bolt face and true to the bore. Fire a few new cases and re-measure the case head run out. If the cases show no run-out then the problem is not the bolt head, it is with the chamber, or possibly the action body is bent.
All of the above assumes the barrel was correctly installed and indexed, and that the rear chamber of the barrel has a full 300 degrees of contact with the corresponding surface on the action body.