I'd vote for a second opinion from a doctor who knows something about addiction.
And I would be asking for the opinion in a different way. Like... doc, I am a chronic alcoholic and I know that some medications are more dangerous to me than they would be to ordinary people. I really don't want to be taking anything that I don't absolutely have to take. I would like to be free of all mind altering chemicals. Is there any way that can be accomplished in my case?
If I didn't want to be free of mind altering chemicals, then I would be wasting my money talking to another doctor. I might not even make too much of an issue with my existing doctor, perhaps letting him know I have quit drinking without directly raising the issue. I can stretch the honesty thing a fair way, I am analcoholic after all.