The OP said, "I can live without rayon, but, dang, I'm gonna miss polyvinyl chloride!" Rayon is made from wood. We make vinyl chloride from petrochemicals, but the original source was plant material and the majority of world production uses plant material. Acetate, is another one typically from plants. As is nitrocellulose. Casein, is a protein from milk. It is also the plastic that the buttons on your shirt are probably made of. So plastic without petroleum is not that hard to find.