I was once recommended T-Cut for cars but have never actually tried it. Has
anyone?

T-Cut is a fine abrasive. It may work but will leave a micro-scratched
surface that's likely to hold dirt and stains. Using a car polish
either afetr or instaed of T-Cut may work but the bath will be slippery
so be carefull. I've used car polish on dulled UPVC windows before and
it works well.

John