Still ignoring how magnetic fields actually work, Tom? Yes, they always form closed loops. But often they start off moving away from either pole before the curve back around, go past the other pole, and curve back once again to meet it. So yes, often enough magnetic fields would just fly off into nothing, with the effect being most pronounced in the vicinity of either pole. I can get the diagram out again if you like.
The problem you pointed out in the previous thread was that if you are directly below the South Pole and attempt to travel Northward, the 3D field lines might curve upwards on themselves overhead of the vessel, leaving the compass confused.
And this is true in many areas south and north of the poles, not just directly 'north' or 'south'. It becomes significantly less pronounced the further 'east' and 'west' you move relative to them, however, and would be most noticeable directly 'north' and 'south' of the poles. The directional bearing is by using a compass rose on the map in this case, just to simplify.
How many ships below the South Pole in Fiji are set their path to travel exactly North, though? Not many, I'd wager. Most will be traveling West, North West, East, or North East towards known landmasses, not out into open ocean.
But even if a vessel happened to venture out too far North from Fiji, it stands to reason that they would see their compass non-functional and decide to sail back towards the sun, either going back home, or perhaps sailing around until catching one of the stray NW or NE field lines which curves towards the North Pole. I doubt anyone would sail blindly into open waters without a working compass.
Feel free to charter a boat and sail from New Zealand to Fiji, if you think it's so rare. If every compass simply breaks, and you don't eventually come near to one of the many island chains due north of both Fiji and New Zealand, we'll call you right. Of course, we'll need documentation and confirmation by a third, impartial party.
In all respects, the bi-polar model allows for navigation from almost all points on the map, except as you pointed out, when one wants to travel exactly North from below the South Pole, or when one wants to travel exactly South from above the North Pole. Unfortunately, it is an assumption that Fiji is directly South of the South Pole. As we do not have a confirmed map, for all we know there is just open ocean at that location. Perhaps Fiji is not directly centered beneath the South Pole as illustrated in the map but a little to the left or right. This would cause anyone traveling exactly Northward from that location to catch one of the field lines and curve around the world to the North Pole.
There are still several travel time discrepancies, as well as the issue of sailing directly east or west nearly anywhere in the Pacific leading you right off the edge. It would, too, because east and west by compass are necessarily perpendicular to north and south.
You have a fair point in that Fiji and New Zealand aren't directly north of the south pole on a given map, but that's an error with the visual and not the concept. There is a place where such is true, and it's actually directly south of Australia, very near to Antarctica in the Pacific. Looking at the apparent bipolar map, with the south magnetic pole placed where it evidently is, the issue still exists with any of the many island chains directly adjacent to Australia and Papua New Guinea. There's also the issue that east and west would be reversed during the trip from Australia to New Zealand and Fiji, as you'd cross the line between the north and south poles.
If your point was that the distance between Fiji/New Zealand and Australia is rather significantly off, again, feel free to charter a boat and record the rate that it took you to reach Australia from either. Get the bearing too, while you're at it. And a third party, we have to make sure the data isn't simply fabricated, remember.
Hence, even if we did find a report of someone traveling exactly North from Fiji (unlikely), we do not even know where Fiji is in the model to say with confidence that the ship traveled exactly North from dead center beneath the South Pole.
So your defence is that, since you don't have a map of the Earth, we can't say your map has the listed flaws? While technically true, the lack of a map at all simply further invalidates your position, on top of the speculative map having so many flaws.