I attended a work shop this past Saturday about this very thing. The instructor did all of her work by quilting her background first. Then added the applique. She had added quilting to the motifs in the design. She had a trunk show of her work. We were to go to the workshop with the background quilted. The emphasis was on the method of applique. It was a great day of learning! So, I would do the cross hatching first and then add the appliques.