Not that I've tried, but I'd heard that toothpaste works. Baking soda and a soft cloth might work too. A very light rubbing compound works too.

Don't you think the cloudiness is inside?

Purchased a product to clean the headlights. It was for 1 car but DH was able to do 2 cars with the materials. One came out fairly well. The other improved but not as much. It was less than $20.

I know this is an old post but bug repellent with DEET works wonders and is cheap.