Hazy headlight plastic

I don't have those, but I was advised to use fine cut paint polishing compound on my vinyl convertible window and it was excellent. No different from polishing dulled paint.

I've tried two different brands on two different cars. Unfortunately I don't remember the brands. It took a LOT of manual labor but they turned out reasonably ok. For me each headlight took one day's work but still better than paying $300 per headlight. Car #1 the headlights were easy to remove and clamped to saw horses. Car #2 would have taken hours to remove so I left them in place. Car #2 did not turn out a good as car #1 but were ok.

I got AutoXS that turned up in ALDI special buys last year. It worked pretty well. Mine weren't so bad that they needed sandpaper, just the polish.

I've had no issues with Turtle Headlight Cleaner & Sealant.

Well gee-golly. Thanks a bunch for sharing that really helpful info ;-)