Phew, I successfully drilled two holes in my fused glass piece so I could attach it to the textile and the mat-and-foam-core backing. In the photo above, I have inserted my long needle and 25# fishing line, so I can mark the spot for the holes.
The fishing line is brought up from the back, through the hole in the glass, and then goes across the glass to the adjacent side and back down again through the textile and backing. To prevent any give in the backing, I attach fiberglass mesh on the back, and tie off with a series of square knots:
For the SAQA Trunk Show, an 8" square opening was prescribed. Here is the finished piece, all matted and ready to ship: