There oughta be a law: Before any "accuracy" work is done the gun must be shot from a Ransom rest. Sure, they may be hard to find, but it is pointless to try to wring accuracy from any gun until it's absolute, intrinsic accuracy is determined, and that can only be done from a rest or a shooter of known quality. Sandbags'll be a start.
I also most strongly recommend that you have another shooter fire the gun. If the problem is apparent across multiple shooters, then it may be the gun. If it miraculously gets better, or worse, it is the operator