If you haven't bedded the action, do so. That is your largest source of flyers. To confirm, take out all action screws and see if you can move the action in the stock. I bet you can move it front/rear up to 1/8" and side/side,rocking) a little bit. It might even rock, tilting high/low. Essentially, there is no bedding in that stock. Just a nicely sized hole the action drops into.
I have no issues with flyers and bed under the tang area. I also fully bed the recoil lug - all sides. I want this area to be an interference fit so the action cannot move AT ALL during recoil. When I put the action into the stock, it should feel like a solid unit with no play, rocking, movement. The screws are only there to keep the action from falling out of the stock - not load bearing devices.
As for action screw tightness, if the bedding is done right AND the pillars are sized properly. You action screws should go from loose to firm tight in under 1/2 a turn of the screwdriver. It should be like you 'hit the wall'.
If there is a gradual increase in tension, something is moving and you are likely bending the action INTO the bedding. Your action screws should never loosen during use,clear sign bedding is wonky).
I would also suggest you bed under the barrel nut and first 2 inches of barrel. That is a heavy pipe hanging off that action and the recoil lug may be flexing. Giving a little support under the barrel gets rid of all action stress and can really help to eliminate vertical too.
Do you weigh your loads to the same tenth of a gr? Many barrels have a narrow tuning spot and a variance of .2 to .3gr is enough to throw shots well outside the group. The case volume of a 6BR makes load consistency even more important.
Do you measure runout in your ammo? If your ammo has runout above 3thou, it might be a cause of flyers,some bullets are more tolerant of runout).
Same goes for seating depth. If you just set the die once and loaded various brands of bullets, you could be well outside the needs of that bullet/load.
Rests, bags, scopes, shooting form/consistency, etc are other areas to investigate to reduce group sizes. Shooting 1/4mins groups is not easy even with a rifle that can do it consistently.
I expect your Savage to shoot 1/2 min, maybe a bit better over the long haul. That is not your best group but average of your worse ones.
If you are shooting in the early morn, consider using a 2ft strip of plastic flagging tape. A normal wind flag may be too heavy to show the light swirly winds that happen at dawn.
Some of the toughest air I have shot in has been at dawn. Twirly, switching enough to push shots outside the teeny tiny groups we expect in 'dead' air.
Doesn't take much wind to push us 1/8" does it.
Jerry