Easy way to do it, just ban Cardinals in the major league draft, minor league draft, and from the waiver pool, and ban them if a team drops out of the league and has some still on their roster.
You'll still have an occasional Cardinal slip through because they sadly got traded to that god forsaken rathole city and the teams that might want to keep Goldschmidt or Flaherty, but at least we're still keeping most of them out.