for making windscreens and helmet shields look brand new, seriously, try Novus.
the prices are way better than similar auto targeted products (amazon has 64oz containers for less than auto places sell 6oz ones).
i used to use this on acrylic fish tanks back in the day, and just happened to find a couple of partial bottles the other day. i used it on my stock screen and helmet shield this past weekend and OMG, presto! (ok.. in reality.. 10 minutes with a buffer) like new. 5K miles of wear = gone.
novus comes in three formulas. #1 more of a cleaner/polish, #2 for light scratching, and #3 for heavier scratches and heavy UV haze.
while #3 says for heavy scratching, i highly recommend starting with it, even for light scratches. once the scratches are gone, finish the job with formula #2 (much lighter grit) to buff out any haze that 3 could leave behind. you could use #1 at this point, i've yet to see the need to take it there though.
for application, using MICROFIBER cloth over a buffer or a drill with a buffer pad is BY FAR the best way to work out heavy scratches or large scratched areas. again... you have to use microfiber cloth. also, doing it by hand sux,
it basically pays for itself after renewing 2 face shields and can be used on car light lenses <insert acrylic whatnot> too.