I wasn't trying to be snide or dismiss your points out of hand, but I've already agreed several times that that map is diagramming connections between ports and not recorded trajectories. I'm not sure what I'm supposed to have misrepresented.
I have stated explicitly what you have misrepresented. I am not going to repeat myself
ad infinitum just because you are inexplicably "not sure" what I have said.
I'm merely demonstrating that there are established shipping routes between Southern Hemisphere ports. Tom said that there those routes are not traveled as frequently as Northern Hemisphere routes. Neither of you have at all explained why that matters (likely because you'd have to assert without warrant that those routes are somehow less predictable), and I provided a direct quote from the source that says that not all maritime traffic is included in their data, only large cargo vessels, and only those equipped with AIS equipment.
The reason for the disparity in traffic is fairly obvious: the largest trading partners in the world are all in the Northern Hemipshere. It's merely a byproduct of political geography. It's not because those routes are any less understood.
Who here disputes that such routes exist? Who here has ever disputed that?

You have not provided any actual data of recorded trajectories or port call data with which I can confirm that distances/travel times are consistent with RET predictions. You're just assuming that the AIS data used by your source agrees with you.
Not a direct quote, obviously, but I think this is the crux of your argument regarding distance data. True enough, I do not have such data to show you. It's expensive. I'm not suggesting that you have to buy it, but I have little incentive to do so. The reason is that my original argument is not that I can verify with real data that these distances are accurate. My original argument (well, my original snide remarks, anyway) was that those who do have the data, and those who rely on such data to get from A to B without getting lost and dying in any number of horrific ways, all agree that the data unambiguously verifies the relationships describes by a globe.
Do they? Or is this an inference you have made, rather than a contention made by any of the sources you refer to?
Would you mind elaborating on this point? What do you mean by 'functional?'
Start with Longitude. It's true that people have been accurately navigating before the invention of AIS. However, as Longitude details, before the invention of a method to accurately measure lines of longitude, nautical navigation was totally haphazard. Determining one's location east/west of any reference point was almost completely guesswork. It's difficult to overstate how significant this ignorance was to every ocean navigator before the end of the 18th century. It's also difficult to overstate just how common it was for ships to wreck on dangerous shores miles and miles from their intended destinations, or to be forever lost at sea, or for whole crews to starve to death on the open ocean. Crews that made it to port rarely arrived at their intended destinations. Those crews were often decimated (+50% mortality rates) from getting lost at sea for weeks at a time.
The fact that these problems are solved by position measurements that require a round, spinning Earth to have any meaning at all is, in my view, good evidence in favor of a round, spinning Earth.
The previous systems of navigation also assumed a round Earth. The rotundity of the Earth is not the crucial factor here - it's not as if the Earth became round in the 19th century. Rather, instrumentation became more accurate, and the means of travel more reliable. This is a process that has been going on for thousands of years, irrespective of what shape people believed the Earth to be.