I've polished a lot of plastic as I used to do a lot of polyester finish repair on pianos and polished keytops. What I used is my faithful Makita rotary but instead of using the flat part of a foam or wool pad like you would use on a large flat paint finish, I used the edge of a loose 10" cotton wheel (it looks like a metal polishing wheel but those are stiched, for plastic polishing they are loose or unstiched) and plastic rouge. You have to move quickly as the slightest heat build up can distort/melt the plastic and set the rotary buffer at the slowest settings. You will be amazed as to what that can do. For those that already have a rotary this is a small investment (about $10 for a good wheel and rogue is also cheap). Here's what the wheels look like -
Here's what the rouge looks like -
Here's what the rouge looks like -
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