Okay, I'll see how I go trying to explain this here....
Within NLP there is the concept of "anchoring", in other words using one set of circumstances to trigger a particular response. This can be done verbally (with a particular word, phrase, tonality etc), or kinetically (typically with a gesture, touch, movement, or other action). Thing is, though, although most think of this type of thing as looking to manipulate other people (I touch your shoulder, you feel sad, I touch your hand, you feel happy....), it is far more powerful, and originally designed, to be used on yourself. You literally "program in" the response or action you want in any particular set of circumstances. That's kinda the way this works.
In essence, you train yourself that as soon as you feel adrenalin, your triggered, or anchored response is to adopt a Mushin state, suppressing emotional extremes, and quitening your conscious mind. The way this is achieved is to experience it, deliberately triggering your adrenalin (in a small way to begin with), and then will yourself to adopt the Mushin mindset. As you go along, the adrenalin gets more and more "serious", and you take less and less time to adopt Mushin. The ideal, obviously, is instantaneous adoption once adrenalin is triggered, but that is a long-term approach, not something done in one or two sessions, and certainly not by only paying lip sevice to the concept of Mushin that I have seen a number of practitioners do (mainly Western proponents of Japanese systems who don't really get what Mushin is in the first place).
What it is not is suppressing the adrenalin dump itself, though. It is a method of using the adrenaline's strengths and benefits while limiting it's less-useful aspects (in a combative sense... it should be remembered that adrenalin is a survival trait in us, and that is more to do with escaping predators than fighting en masse battles, or even duels or bouts). With the LEO's, and similar, it's not surprising that they look to simply ride the adrenalin and then gradually take control, as that is far more immediately accessible to most people. And LEO's require something that they can take out with them on the street now, not something that will take years to develop.
Mushin goes far beyond that. Personally I see it as part of the personal development that exists within the martial arts themselves, something that takes a lot of time, a lot of effort, but has huge rewards. It is certainly no "quick fix", though! In regards to your comment about "sometimes you get the bear, sometimes the bear gets you", that remains true, but the longer you do this, the more experience you gain, the better you get at it, the less the bear wins.
With your kata, I may suggest that if you are only experiencing "stillness" at the beginning and end, you might try maintaining it throughout the entire sequence. Typically, the idea is to adopt Mushin at the beginning, use that throughout the entire kata, then end with Zanshin (Mushin with a follow-on spirit, one of awareness). In the sparring, you aren't experiencing adrenalin as you are (unconsciously) recognising any danger present. My guys know me (or are at least fairly familiar with me, I should say), and know that they are safe with me.... but I can and do still get an adrenalised reaction in them when I need or want to. In fact, last week in class I was discussing this concept (we've been looking at it via sword techinques), and one of the students mentioned it in relation to aggression. I adopted a Mushin state and just looked at them. This was while I was sitting in the front of the class, and the rest were seated looking at me. Within a few seconds there were half a dozen students shifting rather uneasily, trying to avoid my gaze, basically feeling a little surge of adrenalin, as they were unconsciously recognising the danger I represented. To be absolutely frank here, sparring is rather useless for adrenlin training, as it is always seen as "safe", and therefore doesn't trigger that survival part of yourself. Danger needs to be felt.
In terms of methods we have, there's a few. They are all based around the above concept of experiencing adrenalin (through exposure to danger, or at least recognising danger on an unconscious level). That can be anything from physical techniques in class to certain visualisation methods we use as well.
As a demonstration, again last class we were going through sword techniques, which were a fair bit longer than the class were used to, involving a fair amount of back-and-forth between the two partners. I explained that what I wanted was for the students to be able to maintain a Mushin mindset throughout the entire technique, so don't worry about going fast, just take it at a slow pace. Walking around, I saw that no-one was actually doing that, they were consciously thinking through the movememts instead. So I acted as the "attacker" for a number of them, still at a slow pace, but commited and without any pauses. Every student I did that with at some point completely froze, not sure of what to do next, even though we'd spent about the last 25 minutes going through it repeatedly. I pointed out that that was a lack of Mushin showing through there, and now they were to train without thinking through the kata, just reacting the way the kata taught. There was a marked improvement each time, due to the fact that a sense of danger was introduced, allowing them to actually understand and experience what Mushin is about. Without danger, there is no growth in martial arts, really.
