How long are you making your stems to have a seam in the middle? Or did I read that wrong? I have done a bit of applique stems and never had a seam. Try cutting a piece of fabric 1 and 1/2 inches wide and however long you need out of one piece of fabric. Follow what MarLeClair said about stitching one side down and trimming the seam allowance down and then turning the other side down and stitching it down. You'll get it.
Becky Goldsmith from Piece O Cake has several very good video tutorials on YouTube about applique. I would look at those to get some pointers. Good luck.