The answer, steeks. Problem solved and I learned a new technique, too. I was so scared to try steeking, but it ended up being a lot easier than I thought (the fact that this project was only a half skein's worth of knitting, rather than a complicated fair isle piece helped, too.
I used this tutorial which was just right. Lucy Neatby's tutorials have helped me out a few times now. She words things just right and makes knitting seem easy for me. I think it's probably time to invest in some of her DVDs.