Need help with horizontal stringing

I have a rifle that shoots extremely well at 500 yards, usually under 2 inches. When I move out to 1,000 though, the groups string badly and normally move to the right, further with each shot. The elevation is always very consistant but shots will move several feet to the right the more you shoot.
I did find a spot in the stock where the forearm was touching the barrel on the left side. I floated it and will try it soon. Do you think that was my problem or could it be something else?

i'd float the barrel and then glass bed the action. some my lighter barreled rifles have the first 2" of barrel bedded.

I always bed the actions as soon as I get the rifle back from the 'smith. I'll try it again this weekend and see if it clears up.