IME with hunting weight barrels, bedding the action and the first 4" of the barrel has given me the best results. Bedding the first 4" of the barrel has made an improvement over a free floated barrel enough times to be a go-to option for me.

I have added pressure to the barrel and only noticed a change in the POI, not so much in the ability of the rifle to group.

"Give a lazy man the toughest job, and he will find the easiest way to do it"