I think I would add a border before adding binding. That way you could ease the stretched edges of the quilt into the border and have an unwavy edge for the binding. You would need to cut the border pieces to correct size first (measure through middle of quilt).
Also, depending on the fabric used for the border, it would help to heavily starch the border fabric before cutting to size so the border pieces remain stable throughout the process. (I use a 1:1 solution of Sta-Flo liquid laundry starch and water, saturate the fabric, toss in dryer, and iron.)
I love the way you put the pieces together. It will be a great quilt!!!