FWIW, rather than having a real compost pile last year, I was just throwing my kitchen waste in an unused spot in the garden patch. (Grass clippings and autumn leaves went in a separate pile to use as mulch.) I tilled in a couple of those corn oil-based salad bar containers, and haven't seen any scraps of plastic this year. Maybe it's just broken up into very small pieces and not actually biodegraded yet, but as long as they're nontoxic, I don't suppose it much matters.

Cornstarch packing peanuts are water soluble. I have plenty of the EPS ones to reuse (plus I didn't want to leave any potential mouse food around the house), so I just threw the starch peanuts on the pile and they soaked into the ground with the first rain.