There are two ways to tune a rifle for accuracy.
By hand loading and varying the amount of powder to control barrel vibrations.
Or by tuning the rifle to shoot one specific type of military cartridge, with bedding and up pressure at the fore end tip.
A standard Remington 700 rifle is not free floated and has 3 to 9 pounds of up pressure at the fore end tip.
If you free float a barrel that wasn't free floating to begin with your are "taking it out of tune" and changing barrel harmonics.
At the instant of firing gravity and chamber pressure starts the barrel moving downward, and normally on the up swing the bullet leaves the barrel. If you can control this movement and get the bullet to leave the barrel at the exact same point of barrel movement you will have a small group size. If you have "bad vibes" you will shoot "bad" groups.
Example, in the photo below a No.4 Enfield at 50 yards stringing is shots vertically due to lack of up pressure at the fore end tip caused by wood shrinkage and the trigger guard bushing being too long.
Below the same Enfield rifle after re-shimming the draws area, and readjusting the forward trigger guard screw bushing-collar. This gave the Enfield rifle the required 2 to 7 pounds of up pressure at the fore end tip that controls barrel vibrations and thus accuracy.
I have owned one rifle that came from the factory with a free floating barrel a Winchester model 70 with BOSS an adjustable weight at the end of the barrel used to control barrel vibrations.
Bottom line the average rifle shoots better with up pressure at the fore end tip and free floating the barrel just adds to your troubles.