I found a new product at Home Depot (hanging on a display rack by the sinks). It’s called Hope’s Cultured Marble Polish. Not sure how it would work for you, but it claims to clean and remove superficial stains from marble. There’s no harsh abrasives in it, no wax or silicone. It does leave a very high gloss, (much nicer than paste wax) and seals/protects the marble. If it doesn’t remove the surface abrasion sufficiently, it would certainly be a good polish to shine up and protect the marble once you get it smoothed out.