What Latrinka said. I have also had issues doing it the way you have described. I also have better luck with a stiffer home dec type NON fusible rather than a soft batting. Using a fusible makes the process less forgiving because the fabric is trapped by the adhesive.
As far as the 3" blocks are concerned, how about if you used two 9" (finished) blocks, then put a 3" X 18.5" solid strip on the bottom? You could coordinate the bottom fabric with the handles. You would need to seam the bottom so the sides come out on the seam between the blocks, not the center of a block as in your top photo.
Or you could also use two 6 inch blocks surrounded by 3" plain strips, then seam the bag as in your top photo so the plain strips are on the sides. Sorry about defacing your beautiful square in square example, but this is what I am thinking of
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Quilter's Cache is organized by block size so you can easily find blocks of appropriate size.