Generally speaking, the 2.75" slugs tend to be more accurate in most guns so I'd continue my ammo search there.
The lead sled "can" be a problem with consistency in that it inhibits normal recoil. I would use regular bags and see how that works.
I would also let another experienced shooter try a few rounds from your gun. It's very easy to develop a flinch without realizing it, especially with heavy slug loads.
Finding the most accurate slug for your rifle can be expensive but I'm sure you'll get there. The Federal Barnes X slugs proved to be the most accurate slug in my Rem 11-87. It was the last slug that I tried. Go figure.