Update: Proof you can polish a turd
I am making some progress. The finish was already scratched in a few places and was heavily covered in some spots. I'm using a bore brush on a rod with the car wax/cleaner as a lube. After I started I realized any lubricant would work because it's just sticking to the paint that the brush is working up. I'm also using an old T-shirt to wipe away the wax/paint mix. A good stiff brush of some type would be less abrasive but someone had already done a terrible job of trying to take the paint off and this is never going to look brand new without re-finishing it.