Here is what Dupont recommends for Corian care:
Caring for DuPont™ Corian®
There are a number of products made for Corian and similar "solid surface" countertops, but I'm not sure any are better than what you are using. Some examples are Stone-ware, Countertop Magic, Stone tech, SCI Deep Clean, etc. My wife likes Weimans, which Walmart sells. Walmart, Lowes, etc. will have at least a couple brands on the shelves in the cleaning products aisle.
As for the color vanishing on your repair, that should not be. The color on real Corian goes all the way through. Either you have left scratches in the surface (400 grit is not fine enough to bring up a good shine) or the material wasn't real Corian. If it is tiny surface scratches that are discoloring it, you need to wet sand with Silicon carbide paper, working your way up in grit to around 600 or 1000. If you want a really high shine, you will have to get glass wool polishing pads and go all the way to 4000 grit.
2004 American Tradition; 2014 Buick LaCRosse
Homebase in the Ocala Nat'l Forest near Ocala, FL