Kurt,
Sounds like quite a project. Hopefully one of the dirt moving experts will chime in with opinions.
We've got some drainable ponds that we drain down in the fall and then seine the fish out of. It doesn't take long for the surface to appear dry, but the problem with silt is that it doesn't have the porousity that normal soils do. Thus it gets a hard crust on top, and there are no pores in the soil structure to allow air (and hence water vapor) movement through and out.
I'm just guessing, but I bet it will take a lot longer than one month to get enough drying and strength in that material to support much of anything. Plus, since you are in IL, you know how wet and humid it can be there in the summer.
I'd think your best bet might be to use either a dragline or a long reach excavator to pull out as much of the slop as you can, and then work in clay from the edge in, pushing it out with a dozer and compressing it to some degree. Then use the dozer to pull the sheepsfoot packer over top.
The bad news is that this is big equipment, which equals big costs.
Bill
