First, a minor part of the disagreement is that if I were to use the chess approach, I would select a much, much more obscure game to use for the passphrase data. With easily up to a million recorded games, that adds another 20 bits of entropy to my BrainSeed. And I think there is more obfuscation possible.
Of course further obfuscation is possible, making it more difficult to remember.
But let's say that the BrainSeed has 75 bits of entropy. In normal BrainWallet cracking efforts, the target is to try derived addresses and check if there is BTC there. However, here the target is to find a passphrase that has to be used in conjunction with another passphrase. So really there is another 75 bits of entropy to deal with. And then the iterative process adds a lot of time delay between each cycle.
(If I understand you correctly) If you assume that cx-xxxx gives you 75bit then cy-yyyy doesn't add another 75bits since it is the same strategy and the same championships. So you only get entropy from repeating procedure: 2bits + 5 almost random numbers (14bits) + bip38 (20) = 36bits.
Second, my real desire here is to create a Brainwallet passphrase with high enough entropy that the standard cracking efforts won't uncover. And with BIP38, they would have to crack another high entropy passphrase to get at the encrypted private key.
Nowadays cracking techniques are becoming very sophisticated. Very huge computers are equipped with databases of human generated passwords revealed in many website leaks. As a result it is possible to uncover most popular obfuscation strategies, words, numbers used to generate password. It is very easy to underestimate current, and most importantly future AI capabilities in this area. Using non standard method is just another way to add entropy, and sth to remember. But it is very misleading to assume that computers wont try to break those non standard methods. And it is very easy to overestimate human generated password entropy.
My point is that while it is possible to create safe brainwallet with human generated obfuscation method, it is very difficult thing to do so. It may be slightly easier to remember, but they require a lot of time to be created. Also, while people can't calculate entropy properly they will never be sure if they created enough of it. Even if you come up with clever and provably safe instructions, most people would just not follow them properly (and the method will no longer be non standard).