Digitising for fleece material.

I have digitised a large Stag of about 28cm wide, for the backs of polo shirts and normal shirts. The design has a tatami fill and a 2mm satin border in another colour around it. Sews out perfectly on the polos and shirts but when I stitch onto Fleece I have a problem. What happens is that the Tatami fill seems to squash the material out and expands the stitched area by about 2mm . When the border stitches it now stitches some 2mm onto the inside of the fill with the fill showing outside the border.
I am using strong cutaway backing and laying down a zigzag understitch.
Any ideas what to do to get the border to stitch in the right place or the fill not to expand outwards?
Earl.