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I lack the long experience with long range shooting that most on this forum have. That being said, I can say without any doubt in my mind that consistency is everything. I have a 700LR in 30-06 that was worked over by an expert and to which I added some trigger improvement. I tried shooting of a bipod, and a pack, and could not get consistent results. Close but never close enough. I finally started using a M1907 Military Style Leather Rifle Sling rigged for shooting to provide stability. I dumped the bipod and started using available supports and my pack and the added pressure and consistancy of hold improved my shooting dramatically. I have since switched to a Ching Sling with increased improvement and consistency from all shooting positions.
I plan to add a Ching sling to a Marlin 30-06 I have but I am a little concerned that on this very lite rifle barrel the increased pressure on the forearm from the sling will warp the barrel. The barrel was not originally free floated, but I have reamed out the stock and bedded the action, so we will see.
I guess my bottom line is that if a truly solid shoulder hold and consistent positioning from a Ching Sling will improve consistency on a 13-pound rifle, it should improve a 6-pound rifle.