For anyone looking to rejuvenate a black plastic part, you may want to look into Eastwood's "Plastic Resurfacer" - basically a very high-solvent spray bomb with some black pigment.
The front spoiler is original to the car and had seen years of use (although not many miles), as well as a bunch of Armor-All and other products. It was in good shape, but the surface finish was a combination of shiny, milky, and matte - so was ripe for a do-over.
I cleaned it really well with Dawn detergent and warm water, then lots of wax remover / degreaser paint prep solvent. After letting it dry for a while, I lightly scuffed it with 400 grit sandpaper and then cleaned it again with the paint prep. After a couple days to dry / outgas, I applied four light coats of the Eastwood Plastic Resurfacer. I was really surprised with the results and would highly recommend the product. It appears to be fairly durable, but time will tell.
Here are before and after pics of the spoiler.