Polinum is the best compound I've used on all jewelry parts to get an absolutely flawless mirror finish. It's awesome for bracelets and cases, etc. I final sand with very fine grit paper - not micro fine, but like 7000. At that point without a loupe you could almost think it had already been buffed. Then the Polinum does its magic.
I've not ever polished the topside of a dull insert because I've never had one but my tests with Polinum on the underside bode well for an attempt. You just need to be consistent all the way around as Polinum works gradually on ceramic so time spent in every spot needs to be the same.
On the plus side, there should be a level of glossiness beyond which further polishing has no more effect.