Before you waste any more time agonizing over it take your design to Kinko's to enlarge it to the size you want. I bet you will discover that the 'fine' lines are bigger than you thought. Just be sure to use a good stabilizer under your fabric.

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

We want pictures when you are done!!