It looks like all the Quilting Made Easy patterns are for quilting--not piecing. Yes, Thangles are a paper foundation for piecing triangles.
I've only quilted over paper once & I used designs I had traced on tissue paper--the stuff in gift bags-- and some vellum. Those are very easy to tear away. Maybe you could trace what you bought onto tissue paper and get your money's worth out of the quilting patterns that way. At one time some quilters were very happy using Press 'n' Seal to trace designs onto and then stick on a quilt to follow but I think getting the little plastic bits out would be just as annoying as your paper.
Another thought is to follow the lines on your quilting paper with an empty needle and then pounce through all the little holes onto your quilt.