A trick I've heard of is to cast-on over two needles held together, and then pull one out, and knit off of the now-loose stitches on the other needle. How big a needle you use as a second needle will obviously affect how loose your cast-on edge looks, so you don't want to use a huge one; a small one works well.
Also, it's harder to do this when you're beginning, but for tight stitches, you can slide the stitch up near the tip of the left needle when working it. It's nice and loose up there (and, of course, prone to falling off while you're working it, which is why it's harder for beginners). But you might try it.
I love that book, The Mitten! I used to read it for Isabelle, a toddler I baby-sat for for two years. We loved that book!