I find Timber Stitching Screws useful for this kind of application. They have a very flat head (which works well with an oversized washer if needed) and the thread is appropriate for plastic. Available from Bunnings... oh, guess that's the wrong side of the world for you
but I'm sure B&Q would have something similar.
As for getting the old screw out... pkr's advice is good of course.
I'd start with vise-grips (Mole grips?) on the head (need quite new ones to have sharp jaws).
Then I'd try cutting a slot as pkr said.
Then a centre punch to tap the head around.
Then might try a drill bit in a drill set to reverse. A screw extractor mounted in a drill on reverse would be a slightly fancier idea but probably no more successful as there's little for it to dig in to.
Then I'd get out the Dremel and grind the head off, expecting to mangle out the plastic thread insert later and replace it.
At least at the end of the day, it's not a particularly critical application - not like, say, an air filter box. Been there done that on a 156