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I did exactly the same stick trick with my son on Saturday. He marked the shadow every 1/2 hour over a few hour span. I double checked with Stellarium when the Sun crossed the meridian and it lined up nicely with the shortest shadow. (Set alt az grid on).
In Sydney the Sun was on the meridian at 13:10 so between 11:00 and 13:00 you hadn't quite got to the shortest shadow. At 13:00 you are 6 deg out. It may make a difference in your alignment.
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