In a stroke of unprecedented luck, it turns out that the (ridge) row gauge for the rainbow pieces exactly matches the stitch gauge for the white in garter stitch. So I can pick up one stitch per ridge, and it is perfect. I find that I love how the alternating horizontal and vertical garter stitch gives it just a little bit of extra structure, avoiding weird stretching.
After knitting the first horizontal panel, I discovered that it really is much, much nicer if I pick up on the second vertical panel and then kitchener in garter stitch rather than another seaming method. It is beautiful, invisible, and not irritating to the touch on the back side.
Remind me again that this is worth it?