Most likely, there are a few things causing your undesirable results. When troubleshooting always start with the fundamentals of marksmanship; are you executing each correctly? How is your follow through and sight alignment? Body position and breathing consistent shot-to-shot?
I sometimes think even the recoil and noise of a .308 can be
intimidating on a subconscious level. This can result in our bodies accomodating or compensating; often the results are undesirable or inconsistent.
Ok, this is going to sound weird, but give it a
shot before disregarding. Try shooting with your eyes closed. Well, sort of. Line up your body square to your target. Place the rifle perpendicular to your body. The rifle should be snug, but not tight. If you can see your heart beating through the scope, it's too tight against your body.
When you think you have a solid position, simulate recoil. Does the rifle move straight back in the bags or does it move to one side?
Is your rear bag straight? When you grip it (not sure what type of rear bag so just assuming it a squeeze type) does it turn slightly to one side--thus setting the rifle up to move in a direction other than straight back on recoil.
Now get your scope on target, close your eyes, take two full breaths (inhale-exhale). This will take your eyes out of the equation and keep them from cheating and allowing muscling of the rifle into position. With your eyes open, it's too easy to make minor unconscious adjustments to keep the crosshairs on target.
Open your eyes. Where are your cross hairs? Have they moved? If so, realign and repeat. If your sight alignment is correct, your crosshairs will remain exactly on target after opening.
Now that your position is correct, it's time to actually shoot with your eyes closed. Yippee!! Repeat the step above. Insure your sight alignment is perfect. Now close your eyes and take two more breaths; this time take the shot at the bottom of your breathig cycle. Focus on perfect follow through. Keep your finger on the trigger. It should be pulled straigt back--imagine a point straight behind the trigger--where your finger, the trigger, and that point all line up in a straight line. Pull your finger to that point, letting it break the trigger as you go. Keep your finger on the trigger all the way through the recoil impulse.
Now open your eyes again. Where have the crosshairs moved? Are they still on target? Right of target? Left? Where is the rear sandbag, did it shift to one side?
Shoot a five shot group at 100 yards using this method. Try to learn something from each shot and practice making each shot perfect. Also, let the group size be the last thing in your mind...your focus in on building correct fundamentals. The accuracy/precision will come.
I relate everything to golf since that is the first sport I really learned. My Dad told me the first day, a correct swing should feel weird and wrong because I've never done it before. He further taught me to not worry about where my ball went--instead focus on doing certain things correctly. And once I was able to put a few things together correctly, my ball would just start to go straight. Same thing with shooting. Build the fundamentals and the rest will fall into place.
Good Luck
PS--or you could always install a muzzle brake and skip learning a lot of stuff


