Never use steel wool on a softened finish. I first clean the finish with mineral spirits, removing all old dirt wax etc. using a soft bristle brush. Use paper towels so you can see when nothing else is coming off. Let dry. Find a spray bottle that puts out a fine mist spray with no droplets. Spray denatured alcohol to the point of run off but not quite. Work on one section at a time. It helps if the surface is horizontal but not essential after you get the technique. Repeat until the surface has almalgamated. Let dry completely for a few days scuff sand and topcoat. I've done many pianos with heavy finishes this way to preserve the original color that would otherwise be impossible to duplicate. Pre-1925 Victors and Edisons can be done as well.
Bruce

