I use our shower, nice pressurised hot water. I use automotive detailing brushes and kitchen spray cleaner (an inch wide paint brush would do) and get scrubbing!
Then, once dry, a good ciffing (the cream) to get any paint and scuffs off, then a buff with aformentioned silicone heavy car polish to shine it up for sale!
The cloudyness is abrasion from the stuff it sucks up whizzing around the palstic. Short of either never using it or cleaning it after every use you wont ever be able to get rid of it, just mask it temporarily.