The suggested approach from A Threaded Needle is genius!
First, you trace your sashiko pattern onto thin fusible interfacing (best to tape it first to stop it shifting):
Then, you fuse it to your fabric, and sew from the wrong side of the fabric, using the traced lines as a guide.
You start with the long horizontal and vertical lines, and then continue doing long rows of stitching at various angles. The aim is to have the stitches about twice as long as the gaps between the stitches, although it's pretty hard to keep it precise!
Unlike other embroidery, you don't use an embroidery ring, and so therefore you actually need to keep your stitches fairly loose so that they don't end up bunching the fabric.
And here is the final thing! It's far from perfect, but for an occasional TV-watching project it was satisfying and I love the end result.