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.
2003 Saab 93 headlamp before repair...
... 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