I embroider most of my labels. I just like that final hand touch and to let the folks getting the quilt know that I loved it enough to put needle hand work on it.
What I would do with the cross stitch is to make it a block. That is, take strips of fabric the same color as the background and stitch them to the sides, then the top and bottom. Turn under the edging like a binding and slip stitch it to the back of the quilt. Then I would take art license to embroider the edges and the joint edges with a decorative stitch because you wouldn't want to quilt through the cross stitch.
Be not afraid to try something, you'll only know it works it you try it! :wink:
Hugs,
Sharon