Hi,
I would recommend you give NA a try. Alcohol is considered one of the drugs, and members aren't going to ask you what you used. I am a member of NA and alcohol was my drug of choice.
AA has been built with a lot of Catholic guilt included. When they talk about God, it mostly is, unfortunately, the Catholic god. NA literature has been written from scratch, and uses either phrases "God as we understood him" or "Higher Power". You can pick anything you like as Higher Power. Here in the Netherlands where I live most people are atheists/agnostics. But the only thing that is required of your HP is that it is stronger than you. Which is why lots of people choose the group they attend as HP -- a group is stronger than one person. Some pick Mother Nature. One person I know picked hurricanes -- they definitely are stronger than one person. Some pick some sort of religion. It doesn't matter. And you can begin your recovery without picking any Higher Power/God/whatever. The third step only goes as far as "Made a decision to turn our will and our lives over to the care of God as we understood him". Not understanding him also counts. And first two steps don't require you to do anything spiritual.
From my experience, which you can believe or not, people tend to discover a spiritual side to themselves once they stop using or drinking. Spiritual does not mean religious. But you might find that meditation or yoga suddenly work for you, which they never did.
If all I said made you roll your eyes really hard, here's another option:
http://www.sossobriety.org/12steps.htmFor full transparency: I believe in a certain set of deities. I do not participate in organised religion of any sort. I very rarely speak about my beliefs at the meeting, and when I do, nobody questions me or tries to change them.
If you have any questions, ask them here or PM me, I'll be glad to help.
Big hugs! (12 Steps meetings of all sorts are big on hugs and I'm no exception. Free hugs!!!)
Currently working on my upcoming signature.