700PSS is headed in the right direction. I've always used kitchen wax paper, cutting a 3/4" strip and folding it back and forth until it's thick enough. Maybe a five-pound pull to make enough gap between the barrel and the stock to slip the shim into place, out by the fore-end tip. Trim with a razor or knife-point...
It acts like the shock absorber on a car, damping the vibrations. The key to tight groups is uniformity of the barrel vibrations from shot to shot. Sometimes, free-floated barrels aren't uniform.
I've done this with most of the rifles I've ever owned; it has always helped get tighter groups.
Hope this helps, Art