I do not know the answer to the interesting questions posed on this thread, but thought I would share what little I know and speculate about.
the five steps 五步 are related to the five phases 五行:
advance, retreat, look left, gaze right, accordingly, are metal, wood, water, fire and earth
I think that the Tai Chi classics differ according to how the five elements are allocated to the five steps. As opposed to the above view, Chapter 1 of the Forty Chapters says:
The Five Phases correspond to advance (fire), retreat (water), gaze-left (wood), look-right (metal), and central equilibrium, or earth. Advance and retreat are the steps that correspond to water and fire; gaze-left and look-right correspond to metal and wood; and earth at the center is the axis around which everything turns.
(Lost T'ai-chi Classics from the Late Ch'ing Dynasty
by Douglas Wile, pp 65-66.) Yang Jwing-Ming has the corresponding text in his book, Tai Chi Secrets of the Yang Style
, on page 37.
I do not know which version the Yangs uphold or whether they uphold both or neither. In the absence of authoritative information, I have preferred the latter version, since I have heard justifications for it. Fire can only advance when it burns. Water always retreats to the lowest place. A farmer holds the wooden part of a hoe to the left and the metal head to the right. Ancient warriors held wooden shields in the left hand and bronze swords in the right. They were wary (顧) of the blows on the left and looked forward (盼) to striking home with the weapon on the right. The earth is under everything.
As for the correspondences in the Tai Chi Treatise, I have a vague and uncertain memory of some explanation that derived from Chinese medicine. I would appreciate it if someone could confirm this derivation or present whatever justification there would be for that arrangement.
I think that the ancient Chinese were interested in correspondences to the five element only insofar as they affected China and its immediate surroundings. To my knowledge, although the Chinese did sail below they equator, I am unaware of them sailing so far south as to reach southern temperate regions. In other words, I am not aware that they would ever have had to confront a situation where the cold regions were clearly to the south and the hot regions clearly to the north. It would be interesting to know what views the Chinese community in southern Australia has.
There would be an even more extreme problem at either of the poles. At the South Pole, all directions are north. At the North Pole, all directions are south. In fact, at any place removed from the equator, north and south lie along straight lines, but east and west lie along curves. The traditional Chinese view of a flat, square earth with four equal directions does not correspond to our modern understanding of a spherical earth.
I only know a little about traditional and modern feng shui, but to the extent that these systems did try to situate humans appropriately in their environment and orient them to such things as sunlight and the position of the sun, it would seem to make sense to reverse the traditional view of fire and water in the southern hemisphere or at least on any land mass primarily in the south.