I used to see these guys in Boston who cleaned a lot of marble statues, benches and building facades. They used steam to get rid of general dirt and if there was heavy sulfation and pollution on the surface they would use lasers which didn't hurt the stone. Marble is so soft that I suspect even a soda blast might damage it.
Good luck and post some pics of the before and after.
Cleaning Talk - Professional Cleaning and Restoration Forum
A forum community dedicated to professional cleaning and restoration specialists. Come join the discussion about upholstery, displays, residential, styles, scales, reviews, accessories, classifieds, and more!