Are there bags combined with method that permit 5 magnum shots from bags maintaining bench position?

Looking for bag recommendation that will fit sporter stocks and the SSS Monte Carlo Sporter slightly wider forearm. Mostly want to improve my hunting site-in repeatability for magnums. Keeping bags in the same spot can only help.

Current experience is with a metal rest that jumps all over and shatters pistol grips during recoil travel. Some time ago one of the "J" moderators suggested carpet foam underneath which helped. Also have a set of light bags that offer little for stability control although cause no damage.

Thanks for your suggestion.