Lying about when, if, and how much they have been drinking is common. Just quit asking and/or trying to force a confession out of him. You can go to bed tonight secure in the knowledge that he is an alcoholic and he lies about his drinking. You will never get him to admit it, so save your energy. It is what it is.
Until I learned how to deal with this disease, I lived in stress and was physically sick, myself. You've given him a list of AA meetings, now find a list of Alanon meetings for yourself. He's not the only one who needs help.