I still have lots of permutations to work though, and don't plan to abandon these series (now at more than 30) any time soon.
But so far the very narrow lines have only served as separators. So it seems inevitable that I would allow the lines to take center stage instead of merely working as supporting players.
I have an idea of how I plan to incorporate this piecing into an overall composition, but a lot of sewing (and pressing) to do first. I'll keep you posted.