So you are embroideing the quilting design? You are going through all those layers? Have you tried an embroidery needle 14/90? Does the thread shread when you just do normal embroidery?
I would set my quilt aside, hoop a test piece of fabric, with stabilizer, and try stitching out the design. I always loosen my top tension just a bit when doing machine embroidery.
One more thought. How old is your thread? You might want to put a tiny amount of Sewers Aid on the thread.
Please keep us posted.