I am wondering if the stiff interfacing would be too stiff and not have enough body to it? Maybe a cotton batting would work? You could quilt the fabric to hold the layers together, and add another design element, or use invisible thread if you want the quilting to be more subtle.
I think (I may be wrong) that you want to some how permanently keep the pieces "fused" together so that the layers don't separate. Isn't their a spray adhesive out now for applique that is permanent? Put out by Sulky I believe?
I believe they are being made with a low loft pellon, which is about as thick as my warm and natural cotton batting is :D:D:D