I am sorry you are having trouble with QAYG. It is a technique that I use a lot. Trimming is very important, because there isn't much slack with a block that has been quilted. The edges need to be the same length, since only limited easing is possible. Equally important is that the edges be straight, because you are butting two blocks together. After quilting the block, I trim it to the desired size and then run a machine stitch around the edge. Sometimes a little bit of micro-trimming is needed at the corners after that. Then things should fit together nicely. I would recommend that you do any squaring that you can at this point.
Your idea of whipstitching the blocks together at this point and then applying the sashing might work for you and allow you to cover a crooked seam with the sashing, but I would never be able to get the top and bottom sashing to match up without basting the layers together. That is easier said than done, because your squares are quite large (hard to reach in that far to the seam while managing all of the bulk).
Good luck with the projects and let us know how it works out.
Dayle