Was Alex really still bad in prison?

I just rewatched a clockwork orange and something caught my attention that hadn't before, and that is how odd it is that Alex acts so good in prison. My theory is that he is not still the way he was before prison as he claims in his narration, but instead he is trying to be a better person because he feels guilt for his murder and is coming in touch with God. I know he as a narrator is saying that he was just reading the bible for the violence, but that seems like a lot of reading just to get tiny snipits of violence and the way he talks to the priest and has memorized passages seems very sincere, so what I'm thinking is that he as a narrator is already at the point where he's gone through the procedure, attempted suicide, and relapsed to being his bad self again, so what he's saying about his thought process in prison is more of an excuse for why he has such good behavior than an accurate description of what he was actually thinking. And there's lots of evidence that could point to this while he's in prison such as the fact that the priest claims he never committed a single infraction in his two years in there which would be very unlike the sarcastic and violent character we are introduced to, he chooses to help out with the church services and hang out with the pastor a ton when If he had just been trying to stay out of trouble he could have just blended into the crowd instead of standing out, and the best of all is the fact that he asks for the procedure that makes him good, I know this seems like it's just an attempt to escape the prison when you think about his motives as if he is a bad person, but I think it's really a sign that he has been reforming on his own and genuinely wants to be good, the Alex that is shown at the beginning of the film would never sacrifice his sexual, violent ways, because he loved being that way, but the reformed Alex that has chosen to become a better person while in prison would want to have his bad desires erased so ha can live a good life. If this is correct then it also makes for a much more compelling character arc, because whereas under the assumption that he is still a bad person in prison his character arc goes from choosing to be bad straight to being forced to be good then back to choosing badness which leaves the impression that his nature is fixed and that unless his has his free will taken away he will always choose to be a violent rapist, under my theory however; he is a much more dynamic character, he chooses to be bad, then he chooses to be good, then he's forced to be good, then he chooses to be bad, which creates a third, more positive possibility for who he can be, this suggests that if you just let a person heal on there own time that they will never need to be controlled by others and that he can choose to be good, as well as bad. Please tell me your thoughts, this might be completely wrong, but I wouldn't put it past Kubrick to use an unreliable narrator and tell viewers something that's a lie.