Could the BSA scope be bad?
Well, I recon! Not all BSA scopes start out bad, but you are subjecting it to as much punishment as conceivable by using it on a slug gun. That broken mount should tell you something!
In addition, many guns will exhibit strange grouping patterns when shot with a recoil-absorbing rest like that lead sled. Could be you are suffering from a bad scope PLUS wild shots off that rest. Change to a scope of KNOWN ability to stand up to recoil punishment. A Leupold will. Then bite the bullet and fire it with nothing but your shoulder to stop the gun from flying away. You won't have the lead-sled withyou while you are hunting, and you need to find out how it shoots w/o the lead sled!
For example, at 100 yards my CZ 416 Rigby (Leupold 2.5X scope) puts its shots into one ragged hole, but when I use a Lead Sled, the hole is about 3" away from the ones shot w/o it. The lower, near-center hole is with the lead sled, the three in the upper right are w/o it.