Have you tried the iron resistant plastic such as
"Perfect Shape" or "Templar". I have found this very good.
You cut shapes then your fabric with seam allowance and dab starch on edges of the fabric and iron over the plastic. Makes really good clean shapes. I have also use a product called "Stable Magic" which is like a stiff pellon.
Same method of turning the edges over but use glue instead of starch. I find I get good clean edges with this product as well. I always put bumps in the freezer paper but many like it.