The chrome paint does not give a true reflective surface. I have painted model cars/trucks with Krylon and polished them out and you could read a newspaper in the reflection. So it is possible to get a smooth glass like surface, but the reflection will be based on that surface NOT on it being like the chrome plating that comes on the light buckets.
Recommendation - find a local vendor that mods/fixes/repairs emblems, such as those that are gold plated. Some vendors can also do chrome plating on those parts - yes plastic can be plated - it was from factory was it not?
Good Luck and let us know what and how you do it - might be a good tech article.