Re: Gripping the stock/barrel while shooting?
I would say a combination of both--but about a 95%/5% combo. Or even a 99%/1%. In my experience, most differences in group sizes in a situation like you describe comes from using different bullets/ammo. I have even found there to be significant changes in group sizes by shooting a bullet with a different jacket makeup than what the barrel has been fouled with. For example, when trying to sight in my 7.82 Warbird, I shot 165gr Nosler Ballistic Tips to zero the rifle, and when I switched to Barnes XLC bullets, the shots went wild. I then cleaned my barrel thoroughly, and tried again with the XLCs--VOILA! 1/2" groups! One thing I always make sure of is to keep things consistent. That way you can remove variables one at a time until you deduce the problem. Clean your barrel down to the metal, and go back and shoot with the bullets you intend to use on a consistent basis.
One quick guess--did you buy a box of cheap ammo to zero the scope and a box of the "premium" to use in the field? I only ask because I've been guilty of doing that in the past, and it ended up causing more confusion and poor groups.
CONSISTENCY + PATIENCE = SUCCESS.
God Bless and Shoot Straight