[jakeru]

I've had great results with Novus products restoring clarity on hard transparent plastic, like plastic taillight lenses. I'd think they would work well on softer transparent plastic, like the vinyl window material as well. I remember using them with a benchtop machine buffer with a cotton wheel and man, it worked amazingly well - and amazingly fast! By hand it would still work, just slower. If you do use a machine (the tool would be a rotary polisher or random orbital polisher), just make sure not to overheat the soft plastic. You might need to be careful at the edges to avoid potential damage to the canvas-like top material. (Wouldn't hurt to tape the edges carefull with masking tape, for protection.)

In summary, I'm quite sure this haze could be restored to like-new and the result will be quite satisfying afterwards. Good luck!