That really is absolutely gorgeous. Something to pass down to future generations, for sure.
I never knew how kitchener stitch got it’s name, so that is very interesting. I can’t remember the last time I did it on garter stitch, but I’ve done some decently long grafts in stockinette. What I find works best for me is to stop after 20 stitches or so, lay the pieces flat, and adjust the tension on those 20 stitches until it is perfect. It is tedious, but oh so satisfying.
For something of this size, that might take ages though. I wonder if there is something you could pin the squares onto something that would hold the stitches in place, similar to a darning egg. My mother used to have something I think was called a “tailor’s ham” that I could see being a possibility. Pure speculation, though, as I haven’t tried it.