I think in your case the sandpaper route would be the way to go unless you have access to a buffer. It doesn't look like they are pitted but those are pretty hazy. The look about as bad as Sennaspirits when I did his a few weeks ago. I got them about 75% better but I didn't want to sand them, I used my PC buffer which did get most of the haze out. I know Meguiars makes a kit, you might want to check that out. If you were here I'd be glad to help you with them. Once you do get them polished I'd strongly urge you to at least once a month use the Plastx and wax/polish them. I also use my spray detailer after the weekly wash.
Pat