I don't do the steps in AA. I just use the group support. I take what I need and leave the rest. That's one of their catchphrases.
As far as turning your will over to "God," I go to an Atheist/Agnostic group. I have learned that various members do various things with their "higher power." Most turn their life and will over to a "program." It's not that the program of AA actually dictates every facet of their life, but rather that in the area of their powerlessness, they use the AA program as their strength and guide and go to a meeting, work their steps, read their literature, they just don't do it the way they used to do it- by drinking.
Another way that some people can work through the steps is by using the guidance of a now dead ancestor as a higher power, and through their spirit and memory accepting guidance and praying for help.
AA's 12 steps support groups meeting are not necessarily out of the question simply because you do not share a traditional belief in God.
I will share some of my unusual path with you. It might help, it might not. I have given way to eastern thought. I don't believe in the God of the Bible and I generally accept science and reject God altogether. But eastern thoughts do not demand that I accept the religious aspect to get the "spirituality." One book that helped some was THE TAO OF SOBRIETY (http://www.amazon.com/Tao-Sobriety-Helping-Recover-Addiction/dp/0312242506) Tao allows for the letting go of attachments to guilt and other "self-condemnation" behaviors that lead to substance abuse. I am not becoming a Buddhist or a Taoist but I appreciate differing views on what spirituality actually means. Tao allows for my beliefs and those of others to be "correct." From other books, I have learned more. I know that in logic, there either is a single all-powerful god or there is not, but by learning the middle way of Tao, I learn that the universe is this moment in time and space. Nothing exists from the past and nothing exists from the future. It is all in the now and recreated every moment. So while I don't let some sky daddy guide my life, I can allow for his existence in some other life. I don't have to be "right" and other people "wrong." That is a very JW way of thinking. But if the universe was just created for this moment, it doesn't matter in this moment what everyone believes about the past and creation. It's just another moment and it will all be gone and recreated again.
Spirituality can be a general belief that people doing good find good in others and others do good for them. There is plenty of bad also, but likened to karma without being supernatural, goodness attracts more goodness than badness. Seeking peace and sobriety attracts peace and sobriety.
My higher power is the acceptance of that force similar to karma- that there is goodness, peace, and sobriety to be found. My higher power is the journey of discovery that is spirituality. I turn my life over to the journey of learning about spirituality and science and religion. Humans are truth-seeking organisms. Instead of scoffing at Biblical or other religious journeys of others, even while I disagree with such a path for myself, I choose to understand why others must be on their path. It has helped immensely with my wife and mother, still JW's.
I hope my ramblings help the tiniest little bit. Also, try googling "atheists in AA" and variations on that to see what others have said.