Todd tends to go with the safest route when dealing with DIY pond owners. I spread gypsum after every drain and refill on my hatchery pond, it raises the hardness, and clears up the water in a day or two. I had great results spreading gypsum in George Glazener's pond 5-6 years ago. IIRC we added 30 tons, shut off the aeration, and the water cleared up in 3 days.

Highfyler and I treated one of my cow tanks with alum and hydrated lime as a test run, and it cleared up pdq. What surprised me was that even with the cows stomping around in it, the water stayed fairly clear for a few months.