Again: I think the test is to replicate distinctly psychological behavior, to come up with theories of how actually-existing minds work, rather than to come up

Again: I think the test is to replicate distinctly psychological behavior, to come up with theories of how actually-existing minds work, rather than to come up with theories of "pure logic" or "pure rationality". You don't do real science by trying to explain your sci-fi imaginings. You try to explain things you've already got in the world.