RE: Vertical stringing ?
Were you resting the rifle on something?
I've noticed that when I make a shot from the bench and it isn't where I think it should be, I bear down subconsciously on the weapon. Now with bolt guns that isn't a problem if they are freefloated and I'm not resting the barrel on anything. But on a BAR or other type of firearm, it could cause you to start stringing upward. I don't see how the sling stud being loose could cause that. Being too tight and touching the barrel can.
Cheapest thing to try is another scope if you have one laying around. Then you'll know for sure if it's the rifle or the scope.
Good luck and keep us posted.