This is a very unusual problem....
Not the poor grouping, but the fact that all the usual fixes (and you have done them) has not had any effect on the group size. Very curious.
Logic (and I love logic, although sometimes it doesn't love me
) says, when trying to figure out a problem with multiple possible causes, you eliminate only one variable at a time. Then see if anything has changed.
right now, you have changed the scope, the mounts, the bases, the bedding, free floated the barrel, then shimmed the barrel for light pressure, and still no change to the way the gun shoots, right?
Usually one or a couple of these things will have some effect on how the rifle groups, and from that effect we can determine what, if anything, else needs to be done. This is truly strange.
Your test with the boresight shows you that the scope reticle is moving after two shots (or 3 or 4). The way to be sure that the problem is in the scope, or the mounts is to shoot the rifle without them. Normally we would say, try a different scope. You have done that, with the same results. Scope fit in the rings (and proper tightness) should not be an issue, but ought to be easy checked. Mount fit on the reciever, again, should not be an issue, but lets look a little deeper.
What kind of mount are you using? One piece? two piece? Is the mount made for your rifle, or is it one that just seems to "fit"? Fit of the rings to the mount is another point. When there is less than correct fit between all these things the mounts may "flex" from the recoil, giving the appearance that the scope is the problem.
You could have the scope & mounts removed, the iron sights replaced and then shoot the rifle. If it does the same thing, then the problem is definately not the scope or mounting system.
You say you shoot from a rest made from a car jack. Make sure nothing is touching the barrel when you shoot, as the change in barrel vibration can cause shots to go "off" opening the group size. You make no mention of how fast you shoot. try shooting over a longer period of time, so the barrel is cool for each shot (if you haven't already) and see what that does.
Your gunsmith has checked the barrel, and says it is ok for headspace, has he checked it for throat erosion and damage to the muzzle crown as well?
You might have him "slug" the barrel, which, if done properly will tell you the actual groove diameter, and can reveal any tight or loose spots in the barrel.
This one is a real puzzler, especially since you have done all the things that ought to fix the problem, short of replacing the barrel, stock (not usually needed, if the bedding is redone, and done right), or the action. The real puzzle is that the rifle used to be accurate, and now is not. If the barrel were worn out, I would not expect the first two shots in one hole, then the rest far away. I would expect a general scatter.
Since you are certain that the ammo is not the problem, I am pretty much out of ideas right now, sorry.
I just had another idea, which may or not be of any use. Put a drop of paint, nail polish, Torq-seal, or anything like that on one of the rings so it covers the edge of the ring and the scope body. Then shoot. If the paint (or whatever) cracks, this tells you that the scope is moving in the rings from recoil. If it is moving, that is a problem, if not, that is one problem you can rule out.
Shoot the rifle two shots, and they go in the same hole, right? What happens if after those two shots you wait a half hour or so, and shoot two more? Do they go in the same hole? Or do they go in a different hole of their own? Or does each one in a different place, right or left?
Have you done shooting from field positions, like standing, kneeling, sitting? Does the rifle group the same way as it does off the rest? or is it different?
I am trying to give you everything I can think of for ideas, in the hope that one of them might lead to being able to identify the cause, but fankly I just don't know. Your rifle does the same thing in the hands of other shooters as well, so it likely isn't you.
Good luck, and let us know if anything else you try works (or doesn't).