When I started using a deeper hook, my accuracy improved immediately. Sometimes when my shooting falls off, I notice that my hook is relaxing, and when I tighten it up, my shooting improves. I put the string in the first joint of my fingers, and then curl the fingertips so that they point sideways, rather than to the front.
I fought this for a long time, because intuitively, it seems to me that you should be more accurate without as much of a hook. I guess the reason I'm more accurate is because I don't have to strain as much to keep the string on my fingers when I use a deep hook. Anyway, it works for me.
To be honest, when I shoot my lighter weight bows, which isn't very often, I find that I may be less accurate with a deep hook. Maybe with a lighter weight bow, I can keep my hand relaxed without a deep hook, and the extra skin just gets in the way. But with my heavier weight bows, the deep hook seems to help a lot.