@chrisw Great! I've got some polishing compounds for car paint that would probably do the same thing applied manually. I'll give it a go.
A few years ago a friend of mine decided to remove the scrutineering sticker on his Zx10 screen using petrol, it turned the plastic to chewing gum and the rag was stuck to it!
Try to get into the habit of putting your gloves over the clocks when filling up or leaving the clocks in direct sunlight.
Good question ! It certainly fogs some types of plastic .... ..... as I found out years ago , when trying to clean stubborn marks on a dvd