Consistency in charge weight is of course necessary. And primer selection can make a difference. However, many of the issues that cause high SDs are found in the neck area of the case.
You should be able to drop a bullet into a fired case. It should fall freely into the case. If it doesn't, where is the resistance? If it's at the mouth of the case, then you aren't removing your burrs completely. If it is at the base of the neck, you likely have donuts (yes, you can even get them in 308 Win.) or a mismatch between neck wall thickness and your chamber. Neck turning solves that. Neck turning will NOT make a significant difference in SDs if there isn't any interference when you're using quality brass like Lapua. Three is zero difference in SD between my cases with turned and un-turned necks.
Make sure than the inside of the neck is polished and completely free of carbon. I just turn a bronze brush in then a few times. If the inside of the necks on that lot of brass still look rough after that, I will put some 0000 steel wool on the brush and spin it in a drill. Several of my friends who are winning precision and F-class matches also so this.
I also swab my cases out with a bore swab. This gets out the junk that's fallen inside, including any lube. This also leaves a residual amount of lube in the necks, which also helps keep the SDs down. Interestingly, a buddy of mine in the US bought some of Bryan Lits's ammo and tooks some of the rounds down. The necks appeared to have been intentionally lubed. I know some guess that use Imperial dry neck lube.