In my first detailing job we would use Cutting Compound the real deal stuff you use for buffing cars. Get it from an Automotive paint supplies shop you can dilute it with water to lessen the cut. Then use a cut and polish or Autosol to buff it right up using flannelet rag or ya old flannys from last winter.
There Is No Easier Softer Way,
Been there done that just did a full circle.