Go to your local body and paint supplier. They should carry a product by Klean-Strip that is called Aircraft Paint Remover for Flexible Plastic. Just be sure to use it in an open space and over plastic, the residue is NASTY! Wear gloves too and as it contains Methylene chloride and Methanol, don't get it on your skin. It stripped the paint off mine immediately even though the instructions said up to a ten minute wait. This stuff works great and one can (18 oz) did one fascia. Now if you find your foam bumper beneath the fascia is crumbling, I built a new one on the old aluminum extrusion using about 7 layers of foam that Lowes sell as cushioned floor mats and coated it w a can of spray undercoating. Better than the original, I think.
Does anyone have a good KNOWN method to strip paint from the fascias? PPG strongly discourages soda-blasting as a method of prep.
Hand sanding seems possible, but impractical in some areas, such as the embossed "DeLorean" lettering.