No stock is flex free and some actually call it a virtue, as recoil is supposedly ameliorated. I don't really believe the problem was with the stock. I think bipods cause and awful lot of accuracy problems. Any rifle the is shot off an unyielding surface(such as a locked pair of bipod legs) will recoil away from the hard surface, and slight changes in level will cause random dispersal of the shots, a levl rsting surface for the legs will lead to stringing and the flex and shooter hold tension becomes the variable. Bipods are great for hunting but bags and adjustable rests are better off the bench.
As an aside. I've used rods forms to attempt to stiffen a sybthetic stock. The forearm was hollow and guite flimsy. I filled the forearm with aluminum arrow tubing. The ends were cut square and sealed. The tubes were embedded in a matrix of bedding compound. The Graphite arrows made now would be even better as they are lighter and stiffer..but they are price prohibitive.. The aluminum shafts were slightly bent rejects and the bends were strainghtened as much as possible and cut out when they could be. Clean the shafts with acetone and allow to dry before bedding and seal the ends of the tubes to keep the matrix as light as possible.