Meguiars do a clear plastic polish in there Pro Range. I use a product called S100 Plastic Polish intended for motorcycle visors but have not seen it being sold for a while. Another one to look into would be Plexus, again intended for motorcycle visors etc, I believe Demon Tweeks, do or did sell this.
Would work by hand rather then machine on the binnacle plastic as it is quite thin and easy to deform by machine.