Why would you do the two step of freezer paper, then stabilizer for the needle turn? I have seen quilters iron the freezer paper template to the wrong side of the applique, then glue the edges and press to the freezer paper. Then remove the freezer paper and applique to your quilt....just seems like one step not needed.
Also, I use fusible light weight interfacing, fusible side down on the right side of fabric .. after drawing the design on the smooth side of the interfacing, DO NOT IRON! Stitch around the applique, cut a slit in the interfacing, turn the applique using a wooden stick or other tool to push the edges out. After turning and smoothing, trim the stabilizer, leaving a quarter inch or so of fusible around the back edge. Place your applique in its position and now use an iron to press in place. Then machine or hand applique. Hope this makes sense, sense I am not great at written instruction.