It's you who don't allow yourself to say the words without awareness – – but why could that be? Contemplate about it, and who knows what happens. Maybe you'll end up holding your head: "I'm a fool to do such a thing!" – But we are on the wrong track, talking about our "brain". We treat the brain as a computer. Come on, we're wiser than that! Your brain is YOU! Your memories are YOURS! It's not your "brain" that blocks you, it's YOU!
If you follow my line, you end up confessing to yourself: "I want to speak fluently because I want to be normal." But why are you craving to be normal? Because you think you're abnormal. Why is that? Because of stuttering. But you stutter because you want to speak fluently. Ah, so you're totally normal! Than your stutter is the biggest foolness on earth! Not a "poor thing", a "disaster", but a dumb mistake!
But can you believe it?! After decades of humiliation, weakness, hiding, stutterer-pride, stutterer-fighting, lot of speaking fluently, lot of success as well? Can you leave all this behind and be again an almost newly born 2-4 year old child who steps into the light of the Sun and speaks out with awareness of the meaning of his words, not the words itself: "I am what I am" ??
To get to the bottom of that, you have to uncover first the brutal feeling, you're life's monster who've been chasing you since you're aware of yourself; because it's not your brain that thinks you're not normal: it's you.
Well, I can't catch it for you. I cought mine once, and didn't stutter at all for days (before that, I'd been almost mute I stuttered that much). It never entered my head. But still the monster was stronger than me – because at that time I didn't fully understand that it is me. Now I'm gaining the courage. Next time I shake hands with him.
Next time I shake hands with myself.
Good luck to you too!
PS.: If you're still young, maybe you should share these thoughts with an adult, one who you look up. He has probably gone through existential issues like this. With his help, you might put an end to your crazy, laughable habit to speak-fluently-to-avoid-stuttering-hence-stuttering. It's really a childish habbit! You can grow it out.