Mr Sheen, and a blow gun
http://www.dooyoo.co.uk/household-products/mr-sheen/
http://cdn.overstock.com/images/products/3/L11183127.jpg
Spray keyboard liberally, wipe keys firmly with soft cloth, they should come up clean, repeat if required then use a blow gun (compressed air from an airline), and blow between the keys, this will blow out the mr sheen that has gone between the keys, and clean and remove the dirt etc.
don’t use to much pressure and you can do it with keyboard in the TR, (better to remove it), but make sure to protect the screen, because it could be cracked with the pin point pressure from a blow gun.
I use this method often with standard keyboards too