So if I understand correctly you embroider the design on what? Tear away? WSS? Make an applique and sew that onto the fabric with a straight stitch right next to the satin stitches? I never used 2 layers of stabilizer, only with Free Standing Lace. Do you use temp. glue to fix the fabric on the wadding? Doesn't the wadding stretch in the hoop?
Sorry, lots of questions