I have to agree with bedding the action. I would also free float the barrel. I have a 300 WM that is built on a Model 98 action a Bansner HITEC stock and a Douglas Light sporter barrel free floated. After a lot of load experiments I found a load that shot the smallest groups around 2 1/2" to 3". Well the rifle went back to the gunsmith for a full barrel bedding job, that didn't work. Next we floated the barrel and added a small pressure point about an inch from the end of the fore end tip. The groups shrunk to about 3/4". My gunsmith then epoxied the pressure to the stock and now it shoots less than 1/2"
This was just the highlights of what we did, we tried a shims here and there on under the action and trigger guard. The whole process drove my gunsmith who is a good friend more crazy than it did me, most likely because I just bought a Savage Model 10 Predator that would shoot .300 to .400 groups.
We usually meet for breakfast once week with another friend a gun shop owner, And I would rib him a little bit saying "boy I wish you could build a rifle that shoot like that Savage" knowing perfectly well he could.
All in all I wouldn't worry about free floating your barrel you can always experiment with pressure points in the barrel channel. I do say again bedding the action is a must another thing I recomend is to also glass bed the trigger gaurd and floor plate if the action is not pillar bedded.