Ever heard of putting a pressure point, such as a cut credit card, at the end of a free floated barrel?

I've got a thin whippy barrel on a gun and it was suggested to me, wanted to know if anyone else had tried it.

Adding a pressure point to a gun that is set up for a free float defeats the float.  The problem with shimming the barrel of a rifle with a wood stock is that a different shim is (theoretically) required with every weather change to keep the preload on the barrel constant.  Free floating gets around this problem.  Occasionally you will find a rifle with an adjustable device near the end of the forearm that can be used to adjust the preload on the barrel as needed - these are more common on rimfire rifles.

Many older rifles made by Remington have a little bump machined at the end of the forearm to accomplish this; I don't know if Winchester incorporated the same feature, bu t niether of my M70's have it.

If the rifle is shooting well, I wouldn't mess with the shim, except perhaps as an experiment to see if you can detect a change in the rifle's performance.  You will probably have more luck by tuning a handload specifically for the rifle.  If you are going to try the shimming strategy, you might as well experiment with varying thicknesses and installing the shim at different locations along the barrel, too.