Vegetate bare soils as soon as possible, as described above.
Be careful the method you choose to clear muddy water. Hay might work, might not...and it adds organic matter to the water that must decompose. You could be trading problems.
Gypsum could be a great idea, have your water analyzed to see the levels of calcium, alkalinity, carbonate, bicarbonate and sulfates.
Be especially careful with alum. Rapid pH drop happens in minutes, once you reach the breakpoint for that water chemistry.

Teach a man to grow fish...
He can teach to catch fish...