Do the Toyota Camry headlight polishers actually work well?

Overall, do those yellowed polycarbonate headlight deoxidizing chemicals or
1600-grit polishing solutions actually work well enough to be
indistinguishable from new?

We bought for a college kid an older Toyota Camry of the early 2002-2006
model vintage where the polycarbonate on the headlights oxidized over time
to a cloudy yellowed appearance (and the speaker covers on the rear deck
are both burned off by sunlight).

The kid has two options, of course, which is replace the oxidized
headlights altogether, or try those "toothpaste & sandpaper" deoxidizing
remedies on the net, which 'sound' maybe a bit too good to be true.
http://www.jpauleytoyota.com/blog/ho...ights-at-home/

While the pictures by the headlight-polishing companies are always
impressive
http://xfactorae.com

Yet, this article says that abrasives will only work on "glass" lenses.
http://www.ebay.com/gds/THE-TRUTH-AB...0945494/g.html

Only someone with actual experience would know the answer to that question.

Overall, do those yellowed polycarbonate headlight deoxidizing chemicals or
1600-grit polishing solutions actually work well enough to be
indistinguishable from new?

If so, which ones do you have the best experience with on Toyota
headlights?