Basketman ... I'm not sure about the exact pattern you are working on, but when I did a raw edge appliqué landscape design, I did not butt my pieces up to each other. I overlapped them slightly (1/8" or less). I then stitched along the edges, as close to the edge as I could get (I did it free motion as they were not straight lines). I used clear poly thread for this step. I did not use a fusible however, I only used a glue stick to keep a set of pieces in place until I could get them stitched down.
If you look close at the picture below, you can see where I stitched with clear poly thread. After the piece was complete, I quilted over (or as near as over) the clear poly with my quilting thread.
The method I used was from a book and video by Nancy Ziemans & Natalie Sewel.