The problem you are having isn't because of the die, it's your sewing machine. Any triangle you sew is going to do this. A single hole plate will help, also make sure your needle size isn't too large, or you are using a dull needle. If you are still having problems, your idea to paper piece is good, but overkill. Don't need to have paper under the entire seam. Just try using a small square of tissue paper under the leading edge of the triangle, & let it stick out a quarter inch or so in front of it so you can sew a couple stitches on the paper then the paper & fabric.