I've successfully repaired my previous Audi's very opaque headlights and a pal's Saab 93's lamps recently. I sanded with progressively finer wet and dry papers by hand up to 2500 grit and finished off with the Meguiars Plastx polish and a really good result can be achieved if the headlight is constantly kept wet and the abrasive paper is rinsed regularly.
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2003 Saab 93 headlamp before repair...
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... and after sanding and polishing.
The result above took about 1.5hrs to sand through the grades of wet and dry and the polishing was very quick - I don't have a rotary or DA which might be more efficient and get an even better result.
I don't think its necessary to remove the lamps from the car - backside of most headlamps are quite delicate and keeping it rigid is easy when its still attached.
Good Luck.
PR