My thoughts!!! How many layers of fabric are we talking about? Did you fuse the first layer and than add more layers? This would mean lots of fusible.
I hand applique and when there are multiple layers, I keep cutting away from the back side and just leave the seam allowance. Sometimes I cut as many as four times depending on the size of the pieces being appliqued.
You could do a similar thing by planning and cutting away extra fusible and leave just the "rim" to fuse. Another idea would be to use lots of spray starch on the pieces to be fused and forget the fusible.
Suzanne