Thanks everyone for the great advice/ideas. And thank you, TJ for the great pictures- I'd be thrilled to get my reflector looking as good as yours!
Over the next few days (as I find time) I'll be starting and finishing (hopefully) this restoration. I think I'll first try my luck removing the old paint from the back with plain pressured water and going over it with a toothbrush. That is, before I'm daring enough to try any abrasives on the plastic.
I just picked-up this silver/chrome metallic spray paint at Lowe's and I'm pretty pleased with how it shines after testing it on a piece of cardboard.
Note that it was 12 o'clock noon, bright and sunshiny when the photo above was taken. My smartphone camera had to dim the background just to properly capture the bright paint on the cardboard.
Lastly, I can't decide whether it'd be better to meticulously tape-off the "porsche" lettering like you did, TJ, and then spray black once the chrome coat has already been applied. Or if it'd be better to hand-brush the black lettering and spray chrome after. Ideas?