BSA,
The first M70 I had, and still have, Would not shoot until it was glass bedded with fore end pressure. Just free floating it would not help. My .243 with the heavy Barrel is not bedded but it is not giving me the horizontal stringing. My 30-06 I just bedded the fore end tonight. I have see others at the range with the same trouble. Guns looked like Winchester left wood in the fore end for pressure but the barrel would move from side to side. I have not had this happen with Remington's. Just wondered if it is a Winchester thing.