Have you though of making a type of sifter with hardware cloth and a wooden frame? Or some other materials? You might be able to place your sifter over a box or wheelbarrow, put a shovel of soil on, then shake allowing the soil to drop under and the plastic to stay above. Of course, the smaller particles might still go through, but it might catch out some of the other pieces. The sifter can be repurposed as a compost sifter for making finer potting soil.