I have an "old School" reply for this particular condition. First of all, pressure beds (where upward pressure is applied to the Bbl at the stock forend) were often used to tame barrel harmonics and vibration. The risk with using this method is absorbtion of moisture in the stock and resulting movement of stock wood that adversely effects this bedding technique. If you have stabilized your wood stock with proper finishing inside and out and have a quarter sawn blank to begin with, you can get reasonable and long lasting results with a simple pressure bed system.
Back in the early 80s, I was a devoute fan of the .270 Win. and studied many rifle shooting articles appearing some 40-50s vintage American Rifleman magazines, some of which delt with this very issue. In an age before the technology that we now enjoy (and suffer from) shooters were getting amazing accuracy by balancing a forend tip pressure bed to find the "sweet spot". I was shooting a Ruger 77 with a good bedded action from the factory and my best hand loads would only produce 1.8 in. groups, floated barrel. I then took a day and spent it at the range in search of the right amount of pressure. Using target paper and stock finish, I found the pressure that worked, then finished my paper layers to preserve them against moisture.
The bed that I created applied 3 1/2 pounds of upward pressure on the barrel, creating the "sweet spot". Any less or any more pressure and groups opened up. At the right pressure, groups went immediately from 1.8 to between 3/8th and 1/2 in. at 100 yards and stayed there for the next ten years! I never experienced a shift of impact or other stock related accuracy problems with rifle in the entire time that I owned it. I was finally talked out of it by a young man who was looking for a good hunting rifle to start his hunting career out with.
Sporter weight barrels often benefit from a pressure bed at the forend. The pressure that brings accuracy can range from 1 to 7 pounds. The rifle will let you know when it's happy by shooting groups that will AMAZE you. Be patient and use good bench shooting technique when you attempt this process. Some folks will tell you that you are wasting your time and that this is not the "best" way to get accuracy... I still employ this method and it still works as well as it did back in the day.