Welcome to SR, Michael, glad to have you here. Congratulations to you on your decision.
Make no mistake about this, people quit drinking every day, and for good, you just don't see a lot of them here on message boards. They are busy and get on with life, I guess.
Set some serious time aside to look at the posts that other people have made. You will be able to take much comfort in reading and identifying with those that are just like you. You can also look to see how these folks have made the transition to sober living.
Some have chosen a spiritual path, believing that a higher power will do something that they cannot achieve by themselves. As a new convert to Catholicism, you will see many parallels to 12 step programs, in particular to the Sacrament of Confession, or Sacrament of Reconciliation as it is known now. An examination of conscience, a perfect act of contrition, a prayers for mercy, absolution and forgiveness, the performance of acts of penance, and the covenant to live in a closer relation with God, all find similarities in 12 Step methods.
There are alternatives to 12 step methods that do not rely on the 12 step concept for sobriety. You can look into SMART, LifeRing, SoS and AVRT to name a few. You mention that you have tried everything other than 'full on rehab'. Did you look into any of these secular options? Any counseling? Have you asked your Dr about quitting drinking?
I hope you find the support and acceptance you are looking for here at SR, and that you keep posting.