Try also pinning the fabric on the outside of the template, about 1/2" away. That way the fabric shouldn't shift when you are cutting. It works for me.
For template plastic try checking with a local school or maybe a library or printing business that has a laminating machine (the kind that does poster size sheets). The University where I live has one and throws away the "scrap" pieces of laminating plastic that they almost always have (there is usually a bit at the beginning and end of each 'job'). They let me have all I want. It is two layers of plastic, cuts easily with scissors, is clear, and is plenty stiff, and did I mention FREE.