RE: free flost barrel
Most manufacturers do not free float the barrels on productions firearms due to cost. There would need to be added steps to check and correct the stocks. I believe wood stocks would be easier to produce and have the barrels free floated than synthetic stocks due to repeatability. I have several guns with factory wood stocks that are free floated from the factory. There are too many variables involved with the molding process of synthetic stocks so many manufacturers create a pressure point either under the front or along the sides of the stocks.
I have heard from many gunsmiths that the Remington Model 700 does well with a pressure point under the barrel about 2" from the end of the stock. Don't know why.
As everyyone has said, I would free float the barrel and bed the action. If that doesn't help, you can re-install a pressure point under the barrel.