Love the quilt. Been thinking about making one, have the pattern, need the confidence. As for the backing you could use the remnants of the batiks (and make a strip or blocks of the batiks in a scrappy look. Place it somewhere in the backing fabric, make sure that it is off center but not too close to the edge of the finished quilt, don't want the square cut off when squaring the quilt.) As for the main fabric for the backing I would try and find something that compliments all the fabrics in the quilt top. With the blocks of batiks on the back you would have 2 quilts in one.