Does anyone have any suggestions, on the best way to update and/or deep clean corian countertops?
Here's a link on cleaning them from Corian:
Hi Joan, you can paint corian: https://www.paintcenter.org/rj/aug04g.php
IMO, considering the cost of purchasing and installing Corian, I would not try to 'change' it by painting it.
The risk that you will end up with one hot mess is very high.
Instead, put money and time into replacing the sink, faucets, and taps.
This is much easier and can be a fast way to update a room.