I already wrote about karate and Zen
in my forum journal. I have to add that I didn't arrive at this Zen state through meditation but by martial arts practice; you somehow acquire it over time as a byproduct via general karate spirit. It's the physical movements themselves that will be teaching you, and I don't think it's possible to translate a Zen state of serenity directly from the meditation pillow to the competition mat - you have to get used to the pressure of sparring or tournaments first. Remaining calm is easy when you're quietly sitting in the comfort of your home with few distractions but much more difficult when you're moving about, attacking or defending. I've found is that once you've learned to deal with physical stress, you'll also be able cope with real-life stress better, such as in the workplace. However, I'm a rather high-strung person by inclination and don't think that martial arts practice has calmed me down much overall. It has other psychological benefits but I guess for genuine peace of mind, I'd have to spend more time on my pillow.
This mental combat zone is effortless concentration not easily broken by an opponent's feints and theatrics. Any posturing as a tranquil Zen master or fearless movie hero will immediately crumble after first contact though, and any forced calm will be ruthlessly dispelled. I always say fighting is like a truth drug, it will brings out your true personality and cut straight through any fakery. Either you have it or you have it not but it's no use pretending.
As you mentioned, conscious thoughts only get in the way, and so do ego-centered feelings. Feeling triumphant one moment and dejected in the other, hoping fervently for victory, being afraid of losing, etc. will just wear you out. The best tournament fighters I've seen possess this stone-cold impersonal fury, like it wasn't about themselves at all. It's a bit like subtracting yourself (= your self) from the equation; I guess dissociation may also be involved here like you've mentioned in your post but it somehown doesn't feel like that. The best fighting moves will always arrive unplanned, out of the blue, like that punch or kick just
had to go there, don't ask me why.
What I've learned from formal empty-mind meditation is that most of what goes through our heads during the day are repeats and reruns and can even interfere with your real-life experience, e.g. making you forget items when grocery shopping because you were still thinking about yesterday's party, that sort of think. Switching off your brain at will is a valuable faculty to have, in my opinion.