For starters, check how you adjust the parallax on the scope. Don't trust the markings on the adjustment, but turn the ring while looking at the target and move your head side-to-side. When the adjustment is perfect, the crosshairs won't move as your head moves.
Next, play with seating depth of your bullets, starting with them back about .1" from touching lands, then, load 5 rounds each seating depth, say .002" closer with each batch, until getting to .002" from touching. If a sweet spot is found within that range, make more batches with smaller increments on both sides of the sweet spot to further find a better sweet spot. You may get closer to touching, depending on pressure signs, but I like a little jump to keep pressures lower and perhaps more consistent.
If the present stock doesn't have pillar bedding or an aluminum bedding block (didn't see either in the factory description), strongly consider pillar bedding or a stock that has an aluminum bedding block (and do an epoxy skim coat over the aluminum for a perfect fit to your action).
Next, bench technique. Absolute consistency in hold on the bags, pull back pressure against the shoulder, and trigger squeeze are necessary.
Wind flags: If you don't have any, make some, or at least use survey tape to gauge the wind at several intervals from firing line to target. Shoot under uniform conditions whenever possible. It's not necessary to shoot in perfect calm, but shoot when all the flags have nearly the same deflection as the previous shot(s).
Sorry, but I don't reload for the .308, so can't give you any pet loads.