When dealing with an ultra light barrel that is whippy and drives me crazy on grouping, I found a solution that is very effective in solving this issue, SOME of the time.
I will assume that you have already bedded your rifle and your barrel is freefloated.
Next, I will bed 2" of the barrel at the tip of the forearm, but I will not tighten the screw all the way down, about one full turn off. Then when the bedding material sets up, then tighten the screw all the way down. You now have a pressure point on the end of the stock.
If you want to remove the pressure point later on, then place two thick pieces of 3M packaging tape in the barrel channel prior to putting in the bedding compound. The pressure point can easily be removed if you find that the results were undesirable.
This method has helped a few guns.
Often I have wondered if the barrel was not stress relieved after turning the barrel down, which would make the barrel walk around.