Well, I found AVRT and it has worked for me. I'm in a similar boat, atheist with no belief in supernatural beings. No 'easy does it' or stretching supine before any sky daddies. ;-) It has given me tools to recognize my addictive voice and make the Big Plan to not drink.
I just passed the 11 month mark of sobriety. No slips and minimal cravings. Perhaps my experience isn't typical, but it's my experience. Maybe it would work for you, too.