Just watched the interview. Interesting stuff
My eskrima teacher (Sonny Umpad) always worked out with music in the background. Anything from ambient to disco (he danced the 'Hustle' in competitions at clubs in the 70s and 80s). It took me a while before I realized that he didn't just change the music randomly, he would choose the appropriate rhythm he wanted to instill in the student. He would put on ambient if the atmosphere was getting too het up during free sparring, for instance, or put something on with a strong rhythm if he wanted to elicit more of a certain kind of movement.
The other thing he played with was to try to get his students to freeze up. He would move and throw strikes in such a way that it was impossible to defend, to find those 'pressure moments' in each student when they would lose focus and control. He would then work around this limit to extend each student's ability to stay calm and keep focus without freezing or thrashing about without accuracy.
It also seemed like he managed to bypass the intellectual, analyzing part of the brain to connect directly with the physical which I think integrated the information into the body much faster. It was all you could do to move, strike and defend and not get cut into sushi, there was no time for internal dialog. It was a very intense and effective way to train, at least IMHO.
The other thing that struck me from the interview in the context of 'being in the moment with a calm mind', was the value of the so called 'Chinese Internal Arts'. Seems like they were onto this idea, of calming and clearing the mind, and learning the ability to 'slow down time' when they developed the practices.
Tai Chi, Hsing-I and Bagua all have standing meditation practices that also have the benefit of making your legs strong and your body relaxed. Bagua has the circle walking meditation, and all 3 systems do their forms slowly (and fast too later on) to further increase the ability to stay in the moment during complex motion. And the added benefit is that the motions themselves are all designed specifically for martial usage. Pretty cool really.