Did you ever try the DE in your filter as Ben suggested? It can help to filter out things that a sand filter may not be able to trap. It will also help you determine if your pump is just blowing stuff through your filter without actually filtering. I hate to say it, but it may just be that your pump is just too powerful and is pushing everything right through your filter instead of trapping anything. Run your pump 24/7 while you are trying to clear the water and watch your filter pressure. If it rises 8-10 psi over your clean filter pressure, backwash, otherwise don't. Keep adequate chlorine levels and only use bleach. Watch that your pH doesn't drop. It is ok at 7.2 but you don't want it any lower than 7.0.
Take a look at this link about cloudy water. Especially note #4.
100 Reasons for Cloudy Swimming Pool Water
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