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Note that the second requirement is a doozy. Many dynamical nonlinear systems are in fact formally unpredictable past a certain threshold. In other words, it's quite common for 'a sufficient degree of accuracy' in modeling a system to simply not exist.
In the domain of human-created agents, your system will often be predictable, because the human that created it had a specific goal. But extending this to humans themselves may end up being problematic for the aforementioned reason- in that case, you're likely limited to probabilistic reasoning no matter how great the abilities of your predictor agent.
Adult humans are also very much human created. That's what the educational system is trying to do.
When you ask a child for the answer to '2+2' they might tell you 'green'. An adult is a lot more predictable because he has learned the 'right' answer.
Our best efforts to teach people to fit the shema sometimes fail but not always.
True, and even much wider than the educational system, but I would probably rephrase to say that this makes human intelligence predictable within narrow domains. A math class strives to make students predictable when attempting to solve math problems, a legal system hopes to make humans predictable in the domain of violent conflict resolution, a religion hopes to make humans predictable in metaphysical inquiry, etc.
But human intelligence itself is fully general (in that we defined 'fully general' to mean 'like me'), so there's not really any form of training or education that can make, or attempts to make, human intelligence predictable across all domains.