Airbus have a standard polar nav mod that allows flight in polar regions with no problems. Not all aircraft have it fitted as standard. To my knowledge there is only one narrow body Airbus with it fitted.
It allows operations in True and Grid, which is an overlay of a grid on the polar region to stop the instantaneous flip flopping on headings.
As for the south magnetic pole, I have flown over it in a light turboprop and an Airbus. It's just off the coast of Dumont d'Urville at the moment. All navigation by then is done in True. GPS's work fine.
Look at a polar JNC. Lost of interesting lines making pretty shapes on it - especially the grivations
