The toothpaste trick had previously no effect so I went mechanical. This is about halfway through.
I used a virgin Harbor Fright wheel (wet with water first) and some ancient white polishing compound.
The stick had dried out and become like chalk, so I scribbled a zigzag area, and spit on it a lot for good luck until it all blended.
The red polishing compound is more gritty.
Medium speed on the drill because the plastic did heat up fast but I used slow movements.
The cotton disk also expanded four times it's width. Maybe I should have soaked the disk. IDK.
This method took 4-15 applications to get closer to crystal clear.
It was "safe' to use.
(read: slow going and ineffective)
I did use 1000 grit 3M wet on the left side to cut the film first, which was faster but that was not magic.
(1500 would have been better.)
Followed it up with Megiurs "ceramic wax' in the blue bottle....which is not magic either and will leave very obvious lines if not polished off instantly.
It does seem to last longer than Carnuba though.
The trees rain sap and dust constantly here.
The "before" side for comparison.
The right side was much worse and had deep splotches of oxidation.