asheryl,
I think the problem may be that typically you would sew the sashing on to the right & left side before quilting, and then you would sew the sashing onto the "short sides" (top & bottom) of the quilt after that.
But perhaps this does things in a slightly different order. In that case, I'd sew your next block (should be an animal with a sashing strip ONLY on either the top or the bottom -- the one with the sashing on top will seam to the top of your elephant block; the one with the sashing on the bottom will seam to the bottom, so you always have your blocks surrounded by sashing on all sides when it's finished). One way some of these QAYG blocks are set-up is to make columns of quilted blocks and then to take a full length piece of sashing & sew each of the columns together with the long piece of sashing between.
Quilting typically is pieced together at intersections, not in the middle of the piece. If you need to make something work, there are two options: (1) pick whatever place visually looks okay to you -- I agree, that's usually the center although quilters have been known to create a secondary design element by irregular piecing, or (2) sew on a 45 degree angle to reduce bulk. Either way, when seaming together for the sole purpose of making the piece longer, you generally want to use a shorter stitch length (1.4-1.6") and press that seam open.