Here are some tips on Vertical Stringing from an old thread:
http://www.longrangehunting.com/forums/f19/vertical-stringing-37853/
"Tips on
Vertical Problems
1. A lot of rifles are muzzle heavy. Some rifles have too heavy a barrel and this causes
vertical problems, especially those who shoot free recoil
2. Firing pin coming out of hole in bolt in the cocked position. This will cause poor ignition. Take bolt out of rifle and look in firing pin hole. If you cannot see entire end of firing pin it has come out of the hole.
3. Firing pin dragging in bolt or shroud. Listen to the sound when you dry fire. If not the same sound each shot something is wrong.
4. Trigger sear too much spring. Hold trigger in firing position and push down on sear with your thumb. If it is hard to push down, this will cause
vertical problems.
5. Firing pin spring too weak or too strong will cause
vertical problems. If you think this is the problem change springs and see what happens.
6. Tightening front sand bag too tight on stock. When you try to pull rifle back by hand and rifle feels like it is stuck in the bag it is too tight. Rifle should move in sand bags evenly, not jerk or chatter when pulling back by hand.
7. Action not level with top of stock running down at muzzle end. Rifle will recoil up at butt end causing
vertical.
8. The load that are shooting can too light or heavy and can cause
vertical problems.
9. Bench technique not same every shot. One example, should against stock one shot and not the next.
10. Bad primers – if getting
vertical try other primers.
11. Bad scope, if scope is bad from shooting
vertical, if you change your load in anyway and
vertical goes away it is not your scope.
12. Rifle not balanced, it does not recoil right, jumps in bag. If rifle is built properly this will not happen.
13. Some stocks are very flexible. This can cause
vertical.
14. Front sandbag too hard. I personally have never had a rifle that will shoot consistent with a rock hard front sandbag. It always causes
vertical or other unexplained shots.
Other Tips:
1. Head on front rest loose. A lot of rests have movement even when you tighten them as much as you can. This can cause unexplained shots.
2. Some 30 mm scope rings are not getting tight enough to hold scope. Scope slipping in rings under recoil. This will cause point of aim movement.
3. Keep shell holders clean, in press and priming tool. I have seen so much dirt in shell holders that cases are sized crocked on body. Also primers cutting primer pockets bigger shaving brass as you seat the primer.
4. Whenever you can, set up so you can load watching conditions on the range as you load your ammo. That way you will be aware of any changes in conditions since your last group and you will be mentally prepared for the new condition.
5. Learn to look at whole field of flags, not just the row in front of you. A lot of times conditions change away from you will cause shot to go out of group before change in condition shows up in front of your bench.
6. When you chamfer the inside of your case necks make sure they are smooth enough that they don't peel jacket material off when you seat the bullet.
7. I see people walking around with case necks turned up in the loading block. A lot of the time there is condensation dropping from the roof of your loading area. If one drop of water gets in case you are in trouble on the shot. How many times have you had a bad low shot when it has been raining and you have been walking around with your cases turned up in your block?
8. Learn to keep head down and follow through when you are shooting each shot.
9. I hear a lot of discussion about low shots in a group and apparently this occurs a lot on the fifth shot. If it is your 5th shot most of the time you can bet you are doing something at the bench.
10. If 5th shot is a problem, which everyone does at times, we do what I call wishing the last shot in. We just aim, pull the trigger, and do not worry about the wind flags.
11. This year alone I have seen nine lock rings on scopes that are not tight. Guess what that does to your group? Make sure yours are tight.
12. When you realize that the wind is your friend you will become a much better benchrest shooter.
13. Practice in wind, not in good condition.
14. Pay attention to angle changes on flags. Even though you see the same color angle changes make a big difference in your groups.
15. The longer you wait between shots when a condition is changing the more the condition change will affect your bullet.
16. If you do not know how to read wind flags or have never seen a wind flag try to shoot your group with the flags all going in one direction.
17. Equipment at bench has to work flawlessly. If it doesn't get it fixed or get rid of it. We need all our attention on wind flags.
18. Learn to shoot with both eyes open so you can see more of the conditions.
19. Free recoil shooters should be sure rifle hits shoulder squarely on recoil, not on edge of shoulder or muscle of arm.
20. Should have your own stool to sit on so that you can sit at the bench comfortably for you.
21. Hunting rifle barrels – do not get cleaned enough. If you keep barrel clean it will shoot better for you. You should clean barrel good after every 10 to 12 shots.
22. Most hunting rifles will not put first shot after cleaning with rest of shots. So after cleaning if you have a rifle that won't group first shot shoot one fouling shot before going hunting or before you shoot for group size.
23. When working up a load for your hunting rifle take your time and do not let the barrel get hot on you."
My own thoughts based on Weatherbys -
Take the action out of the stock, put a bit of Play-Doh under the recoil lug (maybe 1/4 inch worth) and the action, then reinstall action into stock. Use your hands to push the action into the stock ( you don't have to screw it back in) and see how much Play-Doh is still in place. I found 1/4 inch gap under one of my Vanguards recently - different rifle, same company. I've bedded the recoil lug now to fill that in.
Check the pressure points under the barrel near the front of the stock. See if they are equal, or if they show evidence of unequal pressure.
My Dad's Mk V stainless hates to get hot when shooting. Yours may too.
I assume your barrel is clean, really clean?
The crown is good?
The rifle should do better than 6 inches without "having to" swap stocks. All of my Mark V Weatherbys shoot very well using factory ammo, even my plastic stocked ones.