
More on this model (which I think is cool and aesthetically pleasing):
Obviously the Pole Stars work for all lattitudes which is a good starting point.
Stars next to the Pole Stars will also probably "orbit" in the correct, circular way around the Pole Stars (not much head-ache visualising that).
I also suspect (head-ache alert!) that all of the stars at mid lattitudes will also "orbit" the way that we actually see them - in other words The Celestial Equator is probably going to look right (a straight line).
Whilst there is no real South "Pole", there will be a "Southern Circle/Tropic" on which you would always measure your position as 90 degrees south (by star or Sun) so that could be where Scott and Amundsen went (etc.).
I suppose the only problem might be that you cannot travel east or west away fron a real South
Pole (wherever you walk it would be North) ...
But you could walk east or west along your proposed "Southern Circle/Tropic" without travelling north.
I guess that would be an experiment someone would need to do (and I know that Amundsen sent small groups of men a few km beyong The Pole when he got there so as to circle The Pole).
This is a fun thread - let's debate it some more!
Edit: this is probably the most intelligent Flat Earth argument I've come across so far!