Savage 11 FCNS 308 accuracy issue

I recently bought a Savage 11 FCNS .308 Winchester and I am so far disappointed in the accuracy I am seeing.

Before getting the 11 FCNS I already had a Savage 11 Trophy Hunter XP in .223, essentially the same rifle but in caliber .223 and without the accustock. With the Savage 11 in .223 I am getting very good accuracy, typically 1 MOA or thereabout at 100 yards when using good ammo.

With the 11 FCNS .308 I am getting between 1.5 - 3+ MOA with match grade ammo (168 gr Sierra match king in weight sorted Lapua brass with 44 gr and 45 gr Varget). In the latest range trip, shooting 5-shot series I had one series out of six that was close to 1 MOA, the others being closer to 3 MOA or more. This is with a Vortex 6.5-20x50 scope that has worked really well on my Savage 11 in 223.

Does anyone have any ideas for why I am seeing this kind of poor accuracy? I am quite able to get consistent 1 MOA result with by Savage 11 .223 so while it could be me I do not think it is. I am shooting the rifle off a front rest, with a rear bag.

One thing I noticed is that while the barrel is free floated, the stock is very very close to touching the barrel at the very front-left 'tip' of the stock. Depending on the angle it looks like the stock is touching the barrel but when held up to a light you can see it is in fact clearing the barrel but with very little clearance. Less than the thickness of a sheet of paper. Could this be the issue? I.e. that the barrel ends up touching the stock when the rifle is fired rather than free floating?

Any other ideas or tips?

With out making any assumptions about your technique here are some things I would look at.
1 do the dollar bill test, if it clears to the nut your should be good,or just to be safe sand a little out of the barrel channel then do the test.
2 make sure the scope bases and rings are tight. Torque bases to about 30 inch pounds and the rings to 18-20 inch pounds.
3 make sure the barrel is copper free.
4 slow down your rate of fire, you may be heating up the barrel, if the first 2 shots are close and the rest start to open up you are probably shooting to fast.
5 verify the scope is good, check against another.
6 try different powder and bullets your gun may like something else,check your seating depth.
7 have another shooter try it for groups.
I have found my 308 likes 42.6 gr. of IMR 4895 pushing 150 smk's sub .5moa as long as I take my time to do my part.
Good luck