Ditto on the action screw torque having a dramatic effect on the groups plunking in tight or loose, here or there. My rifles are built on the Savage Target Actions, either right bolt-right port or the dual port right bolt configuration. All shoot best with 35 in-lbs front and middle screw, 30 in-lbs rear screw.
Stocks are laminated varmint style pillar bedded with only the action epoxy bedded. Barrels, barrel nut, recoil lugs and rear tang are free floated.
The Shilen barrels I have are accurate, but one is scrap, because the twist is too slow - my fault. Pac-Nor and Brux (if you can get them), and Hart Barrels are less prone to weirdness. All barrels are Savage varmint contour.
Faster twists are in order on all my rifles, as I'm shooting lead-free. Even when using some manufacturer's recommend minimum twist I have had problems with stability and load sensitivity. In one case the 6mm Barnes Varmint Grenade loaded into a 1:14" twist wouldn't stabilize to the point it completely missed a 100 yard target. When I finally had one hit it was completely sideways. Switching to a 1:10" twist recommended by Barnes, it shot around 1.5" groups. Then I tried a 1:8" twist and groups shrunk from .18" to .30" depending on load.
Berger recommends 1:8" twist for the 6.5mm 140 grain VLD bullets, so if you're using a 1:9" "standard twist" that could be all or part of the problem.
Three areas to watch on Savages generally are the recoil lug seat, the front scope base screw clearance and the rear tang free float. Some of the following may or may not apply to the Model 12 action, but is a good starting point. You probably already know all this, but I'll stick it in for other readers, and in the interest of being an insomniac and trying to help.
Watch the locator pin on precision recoil lugs, and check the stamped OEM lug as well, if the locator pin touches the action at the bottom of the relief cut, the lug isn't seating against the action face. The lug locator pin needs to be cut back slightly or a lug with a ball tip pin needs to be installed. That stamped OEM lug needs replacing with a precision lug.
Flat OEM pin vs ball faced pin (Sharp Shooter Supply) recoil lug.
Front scope base screws included with most bases are too long and if not fitted will bottom out against the barrel threads, placing tension on the barrel and ding up the threads, leaving the front of the base loose. If the base is too long it may interfere with the recoil lug as below.
Here the screw has been shortened so it is below the barrel threads and the base has been dressed back a few thousandths behind the action face. Not all brands of bases will be too long, but the screws will still need checking.
Below are the areas that should never touch the stock inlet, even an aluminum chassis. Here the area has been masked with PVC pipe wrap and electrical tape prior to epoxy bedding. Only the rear of the recoil lug should contact the stock mortise. This also applies to my Remington 700 builds using a Savage type barrel nut and precision recoil lug in aluminum chassis stocks. P.S.: I still run the clearances and skim bed the chassis with epoxy on them all.
Most Savages shoot best with the rear tang free floated. The action below has been glass bedded with the tang clear of contact.
I also torque the barrel nut to 40 ft-lbs, with all threads - receiver, barrel shank and nut lightly coated with Pure White Teflon food grade anti-seize lubricant.
http://www.amazon.com/WHITE-31003-G...r=1-1&keywords=Pure+White+anti-seizeIf all this stuff checks out, then you have gremlins, or that's just the way things are.