Are you using a bipod or bench rest? There is a good chance that the extra weight of the can is making the barrel bounce off the stock. The aluminum bedding block in the HS Precision stocks used on the 700VS and 700P does not extend all the way to the bipod or sling stud. And the stock does deflect quite a bit.
It is a time consuming process, but what I did to solve that issue so the barrel would remain fully floated was to hone out the stock in front of the bedding block using 80 grit sandpaper. It's quite messy and requires attention to detail.
You want to be able to slide a fresh dollar bill between the barrel and stock all the way to the chamber area with the can on and while the rifle is on a bipod or rest.
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