And yes the " S " bushing die will straighten out the eccentricity.
That has not been my experience. I was so disappointed when the "S" die didn't live up to the hype I ordered a Forester with a custom neck. Even that die has a hard time making new brass perfectly concentric because the bodies are so under size.
If you are talking the FL "S" dies I have no idea.
As far as Lapua brass goes....I make sure the necks are round.
........yes it will straighten that out, never mind my blabber.