Many, maybe most, plastics absorb water, something I did not know until just a few months ago. One of our local injection molding companies told me that if the moisture content of the plastic parts they ship out is too low, it becomes brittle and breaks easily. They bag the parts (hundreds to thousands of parts per bag depending upon the size of the part and toss in a small cupful of water before sealing the bag.
Therefore, not all plastics will work equally depending upon the various applications. Some may change their characteristics with temperature, time, humidity or applied voltage. Some types of plastics that are wonderful for high puncture voltage per mil of thickness may have a lousy dielectric constant or undesireable dielectric absorption ("soakage" as Bob Pease of NSC calls it). It's difficult to get all the best characteristics in any one plastic. That's why the good RF caps are usually mica or ceramic types. And, of course, ceramics have their own detailed set of problems, not the least of which is awful tempco except for the NP0 types.
Maybe try a sheet of PTFE (Teflon), although I truly don't know about its characteristics either.
Dean