Your approach sounds ok. When extracting plastics, I used some polar and nonpolar solvents. Typically, it was acetone, isooctane, and chloroform. TCE would be a good replacement for chloroform.
There are a couple of references that might help. The United States Pharmacopeia (USP) has a section for plastic. I believe it is section <661>. There is another section-section <88> that might fit. It gives an extraction techniques, although the extract is typically used to dose animals to evaluate toxicity (acute systemic and intracutaneous toxicity). Plastics are one of the materials that extraction conditions are listed for, usually with relatively high surface area to volume ratios. You sometimes see plastics advertised as passing these specifications- i.e. class V plastic. Some of the solvents used would not evaporate readily, although they would be applicable to other analytical techniques.
Even a plastic like polyethylene can have many ingredients, some of which will extract.
Good luck with your project.