Yeesh, radio silence for 2 weeks. Turns out stays involve a lot more work than I thought, and as you go it looks like you are getting nowhere.
To sew the pieces together, first I whipstitched the seams down using a ginormous stitch to hold them flat.
This ends up producing a strong stitch, which lies very flat from the other side.
This is a period technique, as seen here. And hey, their stitches are much bigger and uglier than mine! I should be more sloppy!