I have a 1987 FJ 1200 with what I believe to be an original windscreen. This screen was hazy, scratched and not too attractive.
I purchased Mothers Power Plastic 4 Lights Plastic Polish. It was designed to easily polish and protect a wide variety of clear plastics.
Holy Cow - this was really too easy. The results were amazing, the method was to use two microfiber towels, one to apply and one to polisgh. Ialso hit this with a orbital polisher/buffer with a fiber cover on the applicator. It took every bit of haze off and all surface scratches.
Not a miracle as deeper scratches remain, but are visably diminished. Very little force required to polish out the haze and light scratches. Very fast job, I took all of twenty minutes and only because I applied this three times over, which was way overkill and not required.
I am very happy with this product, purchased at O'Reilley Auto Parts for under $9. I have enough left over to do this job again whenever I need to, for the next ten years I think.