Brick: I'm a big fan of the liquid sandpaper compounds. Of the bunch, my current favorite is NeoTac Khameleon Particle Sand High Tech Ball Restorer.
However..................
I apply it by hand for the ultimate in deep cleaning. I actually alternate between 'Clean and Dull' and Khameleon depending on how much work the cover needs. And by hand, the liquid sandpaper products have little effect on existing polish. I originally polished my Solid Uranium with Ebonite Matte Finish, and even after a year of repeated Khameleon sessions (by hand), the cover still shines right back up.
Stick with sandpaper, scotchbrite, trizac or abralon for work on the spinner -- you'll almost always get a more consistent finish, and most important, you arn't guessing grit.
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"Sometimes, the best move is the one we don't make"