I don't practice mindfulness meditation any more but I practice cognitive defusion-it's a way to see thoughts as thoughts. You'll read more about it in the books I recommended. Yes, CBT does train you to change your thoughts and beliefs and ACT does teach you to distance yourself from your thoughts instead of changing them. I've never fully read "The Power of Now." I've browsed it in a bookstore but got disinterested when spiritual concepts came up. I'm scientific minded so I'm not into that.
I agree with you on the power of now, I had the same problem with it. It was only when I read about ACT that I started to give part of whats written in PON some credence, namely the idea that you don't have to change your thoughts to overcome your problems.
Like you, I would have liked if it were presented in a more logical and less mystical/spiritual manner, and that's why ACT sounds so appealing to me.