I have been hand embroidering for years and years (It was the first home craft my mother taught me.) and never have used stabilizer or double layers of my muslin. Watch some of the YouTube videos and you will see how to hide the "tails" to eliminate the shadowing you are concerned about. Remember, some of beauty of a hand sewn piece is the imperfections that result from hand work. We are not machines we are artists with thread and fabric. Enjoy your hand embroidery project.