I am a fan of the free floated barrel. I took my SAKO Finnbear in 30-06 to CMP Talladega and it puked chunks at 300 yards, in the original factory stock.
The barrel touched on the bottom of the stock, otherwise seemed OK. I did not want to whittle on the factory stock, until I had some practice on a cheaper stock.
I put the action in a Bell & Carlson stock
I "pillar" bedded the front and rear action screws, and I routed out the stock channel, a bunch, and made sure the barrel was free floating from the receiver forward. Well, it shot better, but not great. So, under the theory that that the action/barrel needed to be stiffer (that is, a Hail Mary idea) I added bedding compound under the barrel. That actually improved things.
This rifle is not as accurate as my pre war M70's in 30-06, but it is much better. Based on my experience with these tupperware stocks, bedding the actions in the tupperware stocks, with a good Devcon epoxy, can't hurt, and probably will improve accuracy. And, it is critical that the barrel be free to vibrate without hitting the stock channel. Bedding under the chamber has given more consistent results than not, but, I don't really know why.