Ok, so you've given me enough ideas for tomorrow. Not going to deal with it tonight.
For context, I'm not a bad wheel builder. Every one that I've built has been straight and quiet. It's not like I couldn't do it. These wheels are what came on a used bike I just got. The intersections where the spokes cross are wound together tightly with thread or thin wire. The closest I can compare this with what I've seen is either twisted spoke lacing or when those spoke junctions would get soldered together (I only saw that once, I don't know if it works). They were done by some custom builder in 2001. The bike is new to me and has sat much of it's life. It's possible those junctions are coming loose.
I can hear the sound at all speeds. It's loudest between 12 and 18mph, that's when I'm not going fast enough to create much road and wind noise but the wheels are spinning pretty quick. At 45-50, I can hear it, but barely over the wind. At 6-10, it's pretty noticeable but I'm usually trying not to die up some switchback so I tune it out.
I'll check the spokes again. Maybe even take off the little custom thingamajigs. I'll report back in a day or so.