I enjoyed your descriptions. I do not know very much about CMA. In my own style, Isshin Ryu, we study what you might call 'external', but I have to add that I am spending a lot of time recently trying to do what you describe when contemplating my own 'inner self' as I am applying techniques. This may not be an official or even a taught manner of practicing my particular art, but I am doing it on my own, because it seems right to do so. I suspect that I am far from the first person to do so.
When I take a stance, for example, I am now spending time thinking about the micro-positioning that makes it work or not work, more or less efficient for my body build, weight, and flexibility; in other words, to personalize it for me. I am also thinking about my inner conflicts and mindfulness or empty mindedness that affect my ability to perform the movement that is about to happen. It's an internal as well as external settling moment; a deliberate pause prior to exploding into the next technique. The pause of course, need not be of a significant slice of time, but a mere fraction of a moment.
We talk about dropping our breath, dropping our weight, but we seldom talk about dropping our concerns and mental state. Seems to me that we should, if we can. Even if we do it during training and not so much in an emergency situation, it helps to maximize our potential.
Funny thing is, it reminds me very much of the marksmanship training I received in the Marine Corps. We used an acronym called 'BRASS." Breathe, relax, aim, STOP, squeeze (the trigger). That 'stop' is very important. Maybe more important than anything else. That's the part where you empty yourself and then you become one with the rifle, the bullet, and the target. The finger on the trigger, and the subsequent movement of the bullet downrange, are inevitable consequences of an action that has already been completed in the mind. It will happen because it has happened.
Works for breaking bricks as well. I break them because I already did in my mind. The brick has no choice in the matter.