What about raking the nuts, leaves, twigs and stones into a pile with a leaf rake and shoveling them onto a shaking inclined grate (like this):



so that the pecans and stones roll down the grate into a shallow receptacle of some sort, and the dirt, twigs and leaves fall through the grate. (I'm thinking of a long grate, maybe 8 to 12 feet long.)

The receptacle the pecans and stones fall into is full of water with a spout at one end. Water is continuously circulated through the receptacle by a pump. The pecans float on top of the water and are carried by it through a wire basket where the pecans collect. The stones sink to the bottom of that shallow receptacle.

What I would do if I were you is go snoop through some books on "Manufacturing Engineering" to get other ideas, because this is what you're attempting to do. Manufacturing engineering is the field of designing machines and processes to perform a task in the most efficient and economical manner.