I am pasting a comment below from John in in Australia, which is of great interest for everyone. John can also add more details by commenting to this post.
I have been watching this site on & off for some time and now feel I should have an input. As a retired Avionics Engineer and experienced international sailor who has designed and certified International Airline navigation systems including VLF Omega, Satnav and of course GPS.
I now live in Cairns Australia and intended to travel down to Rockhampton that is on the Tropic of Capricorn but there was no point at our Winter Solstice and I had already used a protractor and pendulum to check the Southern Cross that seemed to 10 degrees higher than expected, confirming your findings.
As we know the Sun should not go further South than Rockhampton, so I used a Lookout above Cairns at dawn on 21st of June 2016 and used the fence rails as a physical reference then. I continued to roughly take sightings after that date on and off when horizon was visible.
We kept moving south ( sun moving North) for approximately 6 to 7 weeks before Sun stopped and changed direction. The distance is approximately 600 statute miles and the locals around here can tell by the weather that something has changed! The technique described here could be used by your readers and I will take sightings around our Summer Solstice and continue the Sun changes direction again.
Keep up the good work.