A compass works on Flat Earth using a radial magnetic field with where there are infinite south poles.
https://www.researchgate.net/figure/Radial-magnetic-field-vector_fig1_309252454
A compass works on the globe theory using a dipole magnetic field with two poles.
You could follow that model by travelling in a south West direction but when you reached the wall you would be at the south pole? You would travel across oceans and my this method the compass would auto rotate 90 degrees