Ian,
I carve little figurines using Corian, and have had good success in finishing my figurines and have applied the same techniques in restoring the finish on our Corian counters.
Corian responds to wet sanding, and scratches can be removed using emory cloth starting from 400 grit and working up to 1500 grit for a glass like finish.
The final finsih is produced with a mild abrasive rubbing or polishing compound and a low speed rotary buffer. I use a 3M product intended for finishing clear coat in body shops.
See the attached Dupont care document which recommends these products:
Use & care liquid: DuPont Final Glaze or Hope?s Countertop Polish