One possibility would be to lay the ties out in the Dresden circle on a square of background fabric large enough to accommodate the whole "plate". Once you have the ties arranged as desired, tack them down to the background, along all their edges, using basting glue (I'd recommend Elmer's School Glue or a washable glue stick). Iron to dry the glue, or just set it all aside for an hour or so.
Then, using a decorative machine stitch or small zigzag, stitch along the adjoining edges of the ties; use a stitch wide enough to catch both ties' edges and hold them down securely. Then stitch around the outer edges of the Dresden plate. You might need to add a stabilizer to the back of the piece to prevent tunneling of the stitches.
If you want to add extra dimension to the Dresden Plate, you can put a piece of batting on the back (instead of stabilizer); the decorative stitching will hold the batting in place. After stitching, trim the batting away from the outer edges of the "plate".
Be sure to post pictures!