I did enlarge the drawing to the actual size I will need. I'm thinking, based on all the suggestions, that I will cut the whole thing out on fusible web, fuse it to the fabric, and then when I am appliqueing it to the background I will use a variable satin stitch (with stabilizer) on the very thin parts--the fused strips will guide me on that. I hope that will work out.
Thanks for all the suggestions. I always get so much help from y'all.
Carol