Brian,
Still haven't been able to talk with Dennis. Frankly, didn't take time to call him over the weekend, but will do it tomorrow. I'll be in the office for the first time in a month tomorrow. Lot's to take care of.
Here's my thoughts on your question. Alum will absolutely work in your lake. For a day. It is definitely not the long term answer you seek. There's too much water volume passing through the lake, and the water's too shallow. Your best long term solution will be to deepen areas that are too shallow, vegetate the watershed, and periodically clear water with gypsum, as needed. Alum is a quick fix, temporary solution to a long term problem. My qualifications? I have worked with muddy ponds, mostly with frustration, for 23 years. I have used alum, gypsum, lime, hay, filters, rearranging water flow, and every creative idea we could think of, over the years. Your lake was not built properly in the first place. A dam was built, with insufficient thought and action given to the lake itself. Poor construction has helped lead to problems. Throw in the fact you have soils conducive to suspending in water, and you can see why the problem exists. I'll be in touch, as soon as I can. Chasing the paying gigs right now.

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