Measuring the Sun’s height above the Earth in this method gives vastly different heights depending on where you are in the world as well as the time of the year. So, either the method is extremely flawed, or the Sun is physically in different places to different people. Which is it?
This also ignores the bigger issues of a near sun/moon system in that it has no explanation for worldwide observance of the moon phases which don’t change significantly in one day while a near moon/sun system would orbit the entire Earth in that day producing different phases very quickly. How would a near moon/sun system produce the phases we can see?
As for the multiverse based on individuals, not on physical universes, can you explain that more please?
With regard to sun dials, there are many different kinds and they look quite different for different tasks as well as needing to be set up differently for different latitudes and season to accurately tell time... Now, why would sun dials be different on different latitudes if the Earth were flat? What are they being lined up against? The surface of the Earth? or another angle?
For more information on sun dials this is a very good site you should read through...
http://sundialsoc.org.uk/old/HDSW.php