I'd be careful of using chemicals to remove paint as it can damage plastic. I think goof-off is supposed to work well but check the label. Headlight lens polish might be a good starting point as its designed to clean up plastic.
If at first you don't succeed fail fail again. (Waldorf and Statler.) 1997 Geo Prizm...DEAD 1984 Mazda RX-7 Spec 7 2005 Dodge Neon
Goof off is pretty strong. I wouldn't use too much of it and be ready with water to dilute it and don't leave it on too long. If you let it sit, it will dissolve the poly on the floor so it can probably do that to the plastic too. Wear gloves.