We ( I work for an oilfield service company with a mud division) researched "soil farming" which is basically spreading this stuff out and then tilling it into the soil.
I think that would work. I'm thinking you spread the dry mud a few inches thick, till it in, then wait for rain or until the moisture is just right. When the moisture is perfect, you compact it with a sheepsfoot roller or similar. Is that correct?
Sounds like it would take a huge amount of mud though.