Done!
Done x 2!! Now I'll make a third, larger pillow, varying the look of the cover.
In order to allow the fabric to create tunnel domes, it was not stabilized. The quality of the stitch still isn't correct. But, after doing a test run on traditional woven cotton fabric which turned out perfect, I know that the culprit is the fabric. I'm guessing that the strong silk fibers, and the poor quality of this particular piece must be preventing the needle from piercing and forming stitches properly.