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Allan, if you're at Coolah tomorrow at 11.57.42 hrs you can hang a plumb bob from the centre of your tripod and the shadow it casts will point to True South, then look up 31.696º and you will be looking at the SCP..... 
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Matt, I love you for this. So many times I have seen on this forum posts about magnetic variation (mariners never use the term "declination") and calculating this to find true south.
Your method is the correct way to plot a true N/S line. Problem is that most people do not know how to find the exact time of the sun's meridian passage. Perhaps Allan was shown this early in his navigation training, but other matters soon overtook it in importance. Maybe one day I will do a post of how to find this time - it may be easily available for any location on the net these days - I would not know.