Marlette,
When I do fusible on a quilt, I cut out a doughnut of the fusible. Just leave about 1/4-3/8 inch around the edge and then fuse that down to the fabric. That way, you only have a small amount of fusible, which takes away that 'stiff' feeling. I have done several quilts like this and people are always asking what I do as my machine applique feels as soft as hand applique. I also use Steam a Seam 2 Lite which gives a softer feel.
I have had no trouble quilting through the Steam a Seam 2 Lite with my longarm. Of course, if the applique is small, I just outline it and don't quilt in it, but by making that doughnut, even if you have to quilt in the applique, there isn't very much of the fusible to go through.