How to polish Corian countertop?
If you're really going to sand it you don't need a polishing compound to finish.  I worked a deep scratch out of a small section using a quarter-sheet power sander, and then worked up through 800, 1000, 1500, 2000, and 2500 grit paper, at which point it had a mirror finish.

(Only problem is it now looks so much better than the other Corian sections, and it would take a full day to repeat the process on the whole surface area.)