Phosphate culprit
I had the same murky water problem after I installed a 260-watt Coralife over my 80 gallon fresh water tank. I was sure that the cause of the algae bloom was the lights, since I had been running them daily for about 12-14 hours daily. After about 2-3 months of almost total blackout, the murky water remained.
Frustrated, I went and asked one of the guys from the LHS. He directed me to the possibility that it might be due to a build up of phosphate in my tank. You see, I've been feeding fish flakes to my community fishes. Apparently, algae loves the phosphate content of fish flakes. The cure he suggested was to keep changing the water once a week. I had been neglecting the water change for about 2 months. After 2 weekly water changes (about 15-20% water of the tank), the water cleared up enough to see the back of the tank. I then did 2 daily water changes (about 15-20%). About 4-5 days after the back-to-back water change, the water completely cleared up.
I too was concerned about adding anymore chemicals into the tank. I didn't use a phosphate test kit before the water changes, but base on my success, it must have been the phosphate. Hope this helps.