I've not done that with fusible but have done that process. Iwas never particularly good with machine applique either until backing web interfacing as you describe. I find if I go very slowly with the machine, using a blanket stitch, I can have a pretty decent end result.
You could use wasable glue to hold them in place while sewing.
Last edited by NJ Quilter; 09-16-2014 at 10:23 AM.