I've machined a fair amount of plastic in my years in the shop and can't imagine taking a cut on a CD that would improve the surface. Have you tried flame polishing? Not that I think it will work, but it is likely to work better than machining. Most plastics don't cut with a shiny surface. Further, it's entirely possible that if you remove material from one side, the CD might just turn into a bowl from the release of internal stress. Let us know if you come up with something that works.
Harold