I'd pick up some epoxy resin and fiberglass cloth, scuff the underside for some adhesion and start lamming it up.
the epoxyglass will stick better than polyester resin (normal fiberglass), its lighter weight, and stays a little flexible so it doesnt crack up like regular fiberglass. a pack of fiberglass cloth from hardware or auto supply will be a little thicker than what I'd usually use for boatbuilding but its a convenient grab and more than enough to do the job. 4 layers of it 2 layers per day (lay up two, next day sand and 2 more layers), day 3 oughtta be ready to install and a whole lot tougher than stock.. or if you dont think so, do another day adding 2 more layers to that. it'll back up the plastic from behind very solidly once done.