Syne Mitchell's article in the November/December Handwoven, "Stash-Busting Scarves," pages 24-26, includes a note saying you can do this kind of random-but-symmetrical warping on a shaft loom and mentions Judith MacKenzie McCuin's method but no details. Can you divulge any more than that?
I'm not sure what Judith McKenzie McCuin's method is, but I have used one that was published long ago in an article in Shuttle Spindle & Dyepot by Dini Moes. I think it had been around long before that, too.
What you do is take multiple yarns, colors, etc., and wind a warp twice as long as the one you want, but with half as many threads and with a cross at both ends. (Luckily, most warping boards have cross pegs at both the top and the bottom.) Then you cut the warp threads at the midpoint between the two crosses and bring the two crosses together so that the first warp thread is on one edge in one of them and at the opposite edge in the other. If you have changed colors randomly as you've warped, they are now symmetrical in the same way as they would have been in that rigid-heddle threading.