What a lovely quilt!
Cross hatching will work in the triangles, but you might also consider using a stencil there, or quilting one of the applique designs there, and then doing some cross hatching around it.
Think about stitching in the ditch for the sashing. For the pieced border, you have seams to deal with and it doesn't look wide, so maybe stick with the single line. Or continue with the cross hatching. If it's wide enough, how about a simple cable ?
I'm sure other people will have other ideas. I hope you post a picture when it's done.
Janet