There are certainly some interesting ideas in there. Perhaps there should be a rule that turning the cube, as a special move, should have certain restrictions. One might follow the example of Castling and insist that (1) a rotation cannot be used to escape Check and (2) a 180° rotation should be made in such a way that the intermediate position does not put the mover in Check. It would also be useful to define exactly what kind of turn is allowed. In the case of a 4x4x4, do you rotate the third plane relative all three others, or the third and fourth relative to the first and second ones?
One slight distraction in this thread was George Duke's "perimetre". At first I thought that it might be a typo, but it was repeated. Then I wondered if it was a typo of mine that was being emulated by others, but I searched my master documents for it and it was not there. The correct spelling is perimeter in British, as well as North American, English. If anyone is interested I can go into more detail.
One slight distraction in this thread was George Duke's "perimetre". At first I thought that it might be a typo, but it was repeated. Then I wondered if it was a typo of mine that was being emulated by others, but I searched my master documents for it and it was not there. The correct spelling is perimeter in British, as well as North American, English. If anyone is interested I can go into more detail.