I believe the recoil moves the LS system inconsistently which produces groups that just shooting off a bag would put to shame. Seen a few wood stock rifles crack at the pistol grip too when contained in a LS, even in a relatively light recoil cartridge (270 Win)
I remain unconvinced that something like the Lead Sled has any real value for building up a load. IMO, any shooter, with a bit of practice, should be able to hold -.5 MOA at 100 yards with a good front rest and rear bag. Bench rest shooters notwithstanding (they're a separate breed) if your load can hold that accuracy you don't need to tie the gun down.