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Point of Impact Shift (Left/Right)

Improper parallax adjustment will also contribute to the problem…
It will. But again 3” in 100 yards caused by parallax is quite unlikely. That’s a huge shift and if you were way back from the scope and shifted your head from far right and then left (an insane example) you’ll get a big shift but I feel 3” is too much.
Parallax is not really understood by many and the manufacturer putting numbers supposedly representing range has only made it more confusing.
 
It will. But again 3” in 100 yards caused by parallax is quite unlikely. That’s a huge shift and if you were way back from the scope and shifted your head from far right and then left (an insane example) you’ll get a big shift but I feel 3” is too much.
Parallax is not really understood by many and the manufacturer putting numbers supposedly representing range has only made it more confusing.
You’re correct that parallax alone is not likely the sole cause. That’s why I noted parallax in addition to the reasons cited in the post by @22BRGUY.
 
Shooting Prone or off a bench rest, bags, bipod?
Big magnums can be very sensitive to body alignment and shoulder pressure.

Has anyone else shot the gun with the same results?
 
Shooting Prone or off a bench rest, bags, bipod?
+1. If off a bench, of what construction? Is it rock solid? Wooden benches not properly braced can sway horizontally. It doesn't take much to make a big shift on target. Shooting a magnum makes it worse if the bag setup is not good, or you are pulling or flinching at all.

I'd be encouraged by the minimal vertical dispersion. When working up loads I pretty much ignore wind (and won't shoot in any significant wind anyway) and concentrate on holding vertical at the bench. In reading the groups, I ignore reasonable horizontal spread. You do seem to have a mechanical or setup problem of some sort, but I do like your minimal vertical spread.
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Shooting off a table. I have one other 300 win mag that I’ve never had this issue before..same scope, base n all. I wondered about the table so I might eliminate it as a variable. I have a front/rear bag I shoot off of. I was hoping to get out tomorrow but it’s pouring here so be a bit muddy in the morning to get out. I’ll try to update this post if I figure anything out with it but it might take a bit as I’m back to work for the week tomorrow.
 
I usually do as Dusty and start with wind but I agree with others that that's too much at 100 in very light conditions. Before doing anything else, if you haven't done so, go over every screw and look for something simple before jumping off the bridge. It's usually something like that. Not a bad idea to change scopes. That really narrows things down in a hurry and you might find the problem while swapping them. Pay close attention to the front base screw. Loosen the back screw on the front base first and see if it wiggles with just the front screw. Common for that screw to be too long and it bottoms out on the bbl threads before tightening the base. It can feel tight because it's bottomed out before it actually tightens the base. Again, simple stuff first, then dig deeper. If you don't find an obvious problem, swap scopes. Go from there before calling anybody. Then call a buddy to shoot it. Still bad...then call a smith if swapping scopes didn't pinpoint things.
Ran into this exact problem with my friends Savage FTR . After much examination and checking , and testing we found the problem was I had put the Action screws in Back-wards . Upon checking them , One measured .057 longer than the other . Put the "LONG" screw in the wrong place , the whole action moves after every shot . And ou almost couldn't see the difference in the screws when they were laying on the bench .
 
This scope was previously on a 7mm-08 and shot with no problems. Today, the first group was 1.5" to the left of the bullseye. The next 5 groups were 2" to the right with no changes to the turrets. The vertical barely changed as the powder charge increased (0.5g/group). I adjusted the windage 2 MOA to get the group back on center. The next 2 groups were on center and then it moved back 1.5" to the left of the bullseye for the final 2 groups.

If this part of the OP above, is all correct, it’s the scope. The scope tracks expectedly with input, but doesn’t seem to have enough spring pressure once there, to stay in place.

After enough vibration, it moves around a small amount. It’s more likely the spring is catching (sticking or binding a little) on something rather than that it is actually bad. I’ve seen trouble-shooting where the turrets are run their full ranges, with both permutations, several times, to refresh the contact surfaces. Easy to do and worth a try.
 
Update: I took the scope in question and put it on my wife's 300 win mag. This rifle with the load I developed has consistently shot 1/2" groups (5 round and 10 round) at 100 yards. I went shooting this morning, using the ammo I reloaded and shot 4 five round groups (both vertical and horizontal stringing) . Not a single group was under 1", with the smallest at about 1 1/4".

I then shot a tracking test. I zeroed the scope on the bullseye first (bullet hit 1/2" right of center and I called it good) . Then I adjusted 2 MOA to the right and held the same point of aim. The bullet struck 2 inches low at 6 o'clock position. Then I adjusted 3 MOA up and the bullet hit 1/2" high. I then adjusted 4 MOA to the left and the bullet struck 3/4" high. I then adjusted 3 MOA down and the bullet struck 1" low. I then adjusted 2 MOA right (which should bring it back to the original zero) and the bullet struck 1/2" left. This is with the previously developed load that has shot good in the past in multiple different temps/winds.

Prior to shooting this morning, I double checked all the torque settings throughout the setup. Based on what I am seeing, it seems the reticle is moving within the scope as the rifle recoils. I've never had this happen before so I appreciate any thoughts.
 

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