There are different "schools" of Zen, just like there are 386 branches of Southern Baptist church.
It looks like John and Brian are approaching the same problem from different angles. Maybe one or both can't see the merit in the other's approach. That's why they are approaching from different angles!
I'm just glad to see two different avenues(IPSC and Bullseye) talking about Zen and shooting. I've been doing both types of shooting for over a year now. I've been trying to 'grok' zen for just over thirty years now. I read Eugen Herrigal's book, while trying archery. Read Miyamoto's Book of 5 Rings, while studying fencing. Lots of books, good and bad, regarding Buddhism and Zen.
Now I hope to get Brian's book soon, since I've started recently both IPSC and Bullseye.
I applaud John's work on the Bullseye site, I've found it very informative and useful on Bullseye so far. I hadn't even noticed before his stuff on Zen. My small gripe is all the Japanese words. Right now, it's a little evocative of Islam, which mandates the follower learn Arabic. Zen originated in India, developed more in China, then was more widespread in Japan, before coming to America. I'm put off by all the Japanese language lessons John includes in his brief dissertations. But still, overall, I'm glad to see the dissertations there, even if I don't agree with everything he says.
Here's a quote taken from John's website that seems more applicable to IPSC than the (relatively) tranquil sport of Bullseye shooting:
Takuan Roshi explains, "Keeping the mind tranquil as it moves in the myriad directions in the midst of uproar and
commotion is true tranquillity. Tranquility in tranquility is not true tranquility; it is tranquillity in action that is the true tranquility."