I am going to add the sashing to each block and quilt along the seam lines like you stated with the backing attached. The individual quilting lines in the blocks won't show on the back, but for me that is okay. I read a lot of comments in the Dear Jane BOM and several have done this. I will have to whip stitch the batting together then the backing can be all in one piece and stitch down the sashing lines.
I am currently doing this on the "Circle of Life" baby quilt and it has worked out great.