Sorry, my original post was confusing, since vertical and horizontal depend on how you look at it. What I meant was lengthwise stripes.
I could have made this afghan like 5 scarves, then put them together later, but I have this quirky aversion to doing that. When a piece leaves my needles I want it to be finished. If I have to go back and put things together later, it takes the fun out of it for me. OTOH, if that method would save a ton of time over juggling and untwisting balls of yarn, I would force myself to consider it.
Yes, I'm doing intarsia, but I never put a name to it before. When I looked it up, I discovered I was supposed to be putting the new yarn over the old, but I've been doing the opposite. I don't know why it would matter, but I'm not going to change it now. It looks fine and there are no gaps or holes where I change colors.
It took me a whole day of fooling around with all the yarn, since one strand carries all the way across and 2 of the stripes are double-stranded anyway, so I have doubles and triples to mess with. I re-wound the double strands together, which helped some, then I discovered the little hairclip idea to keep the balls from unwinding. I use circular needles, so it was also important to make sure all the balls were on the outside before starting the next row. I settled on a simple k2 p1 stitch, so I've decided this won't take any longer than a complicated stitch in one color.
I was really frustrated when I posted this, cuz I've already had several false starts on this afghan, but now I like it and I've finally got it under control.
Thanks for the input.