Tried to change the bulbs in my number plate lights earlier. All the retaining screws are furred and rusty. Cover over the first bulb eventually loosens. But, thanks to these sh1tty fasteners, the phillips screws holding the second cover are now both rounded - so I'm left with only one half of the rear plate lit.

Anyone got any bright ideas on getting these bulbs out without having to dismantle the rest of the car?

I had the same thing two years ago. Besides that it happened in winter at about -15 Celsius, late at night, pulled over by the cops for speeding (only then they noticed that both number plate lights are off!). I was almost late for the ferry from Tallinn, Estonia to Helsinki, Finland, with about 200km left to go, it was dark and no civilization around. Plus the cops were threatening to arrest the car if I dont get the plate lit properly...
Surprisingly, I had the spare bulbs and started changing them right there, using my Leatherman. Of course, the screws were rusty, so finally I had to break one of those bulb covers. I don't think there is any other way, unless you want to take the bumper off.
...and yes, the cops let me go with only a speeding ticket (which was rather heavy), and I managed to get to the ferry right in time.