There is a guy on the T-ABC email list in the US who refurbishes old fountain pens and has a substance which is claimed to work well on this sort of plastic. I haven't heard of him for a bit though I assume he still does this.
You could fry Greg Clarke who posts on the forum with the user name greg. He and his father Chris restore instruments and dash fittings and he might even have a proper brown P type one available.
Yes, I have painted a number of dash parts - switches etc. Krylon makes a paint specifically for plastic. But most of what you will find on the car isn't plastic, but rather bakelite. Ordinary spray can paint works well.