Those deep holes in plastic parts are always the worst. If you have a dremel you have 2 options. Either cut away enough of the top plastic that you can get at the screw to dremel a slot into the top, and unscrew it with a flathead screwdriver. Alternatively you could try dremel just below the head of the screw to cut the screw in half.
if you have a soldering iron you could also try heating the screw to melt the boss it's screwed into. You might have to cut/melt away plastic to access the screw and then apply light rension while heating so that it opens once the screw is hot enough.
I don't have a dremel, but I have a soldering iron.
Just melting the plastic around the screw by heating it might really work. I will definitely try that!