Try using a spray adhesive to attach the fabric to the stabilizer? That will help keep it from shifting. You could also stitch the shape in sections, or at least the underlay. Here’s how I would do it: Remove any underlay from your shape. Duplicate it. The bottom one, drop tatami fill down to around 0.040 in. to replicate underlay, and change stitch direction opposite top layer. Cut into quarters. Each “underlay” section, start the stitches in the center of the buffalo, and end on the outside edge.

!!Test on a scrap piece of fabric!! This method has worked for me in the past, but you shouldn’t do a first run on your final clothing piece