The "peace that passeth all understanding" is to be found in the Prince of Peace. If anyone has called on the name of the Lord in faith, and believed in their heart that Jesus is indeed who He claims to be, then this person is saved, unequivocally. Jesus Christ is dwelling in your being, even the "earthly vessel," has now become in the words of the Apostle Paul, "the temple of the Holy Spirit."
I am under the assumption that you have accepted Christ into your life Ross, so with this in mind I say you only have to look inwardly to His presence within you for this peace. Nothing can rob us of such, except for our own doubts and fears. We must realize that He is indwelling within us so we might truly be "partakers of His divine nature," and if He is within us, then we need to look no further for anything.
You mentioned the 12 step deals, and this is interesting since I was just talking about the main issue I have with such programs as AA today with a friend that just got out of jail, and who has renewed his relationship with Christ. The main problem I have with AA is the fact that they spend a great amount of effort trying to convince an individual that if you are a "alcoholic" you will always be a "alcoholic" and I just refuse to accept this since I hold Saint Paul in much higher esteem than I do the founders of such human philosophies and Paul makes it quite clear in
"2nd Corinthians 5:17
Therefore if any man be in Christ, he is a new creature: old things are passed away; behold, all things are become new."
and this is one of the cornerstones of Christian belief. I am not who I used to be! I was kicked out of high school over a drunk and disorderly episode 2 months before graduation, and most folks would certainly have proclaimed me a devout drunk, but I haven't drank in more than 18 years, except for rare instances where I have taken the Communion Cup with actual wine, and no I didn't immediately want to run out and get drunk after that alcohol touched my lips. AA's has certainly helped many people, and I can only be glad for this, but this hopelessness that others get from it is just the opposite of what Christ offers us, that is a new beginning, and a born again essence.
If you are a new creature, then you don't have to be hopelessly shackled to your past failures, or even your present ones. Jesus Christ is the sacrifice, and the confession of our sins in faith toward Him is all we need to start the day anew once more. Should we continue to fall, absolutely not, but the more important thing is that we continue to believe that God is able to cause us to rise above such failures.