And a close-up, with basting stitches removed. No better.
So I decided to go back to something simpler, and did trials with various weight threads in either a simple running stitch, or the "conversation" stitch that I used on my Regret quilt.
I decided on the conversation stitch (thanks to Mary Beth for the suggestion). I'm using two threads, a dark, dusky blue 20 wt pearl cotton (hand-dyed) in the darker strips, and 2 strands of 50 wt Aurifil sewing thread in a pale yellow-green in the lighter strips; varying between the two holds down the value contrast between thread and fabric. I think this is better.
The quilt is also secured with in-the-ditch hand-quilting in all the vertical seams, done before I began the embroidery.