I was thinking that maybe the easiest way, provided the clay or fine particle content is high enough, is to rent one of those electric handheld concrete vibrator things, used for getting air pockets out of just poured concrete (
https://goo.gl/j7qOhv). I don't know if you have these out there in America, but it's a fairly simple motor with a flexible part to shove into any foundation pourings. It works very quickly, so you need to keep it moving or else the concrete will separate into its different components. Now that is just the thing you need. Sepp Holzer in his video explains that he puts the bucket of the excavator into the soil and then moves it back and forth to get the soil to stratify. I'm guessing that concrete vibrator machine thingy would do just the same thing with little effort.
