Very impressive. I would love to take a few minutes one of these days and go through what you posted. I just skimmed through it quickly now. Thanks for taking the time to post (and of course do the initial research!).
I just asked the relevant questions. The real work was done by
@dirah, who is incredibly passionate about questions of zmanim in unusual places. I'd love to see him write a book on it one day! We also still need part 2 of his guest post on the trip's zmanim. Not that I'm any better at finishing that TR.
I came to Antarctica with my own book of potential scenarios based on coordinates as we were told there would be no internet signal.
In the end, we did have slow but useable internet, which made all of that moot.
The real game changer was having to divert to the Falklands, which ensured we wouldn't travel far enough south for there to be a shayla according to shitas harav. On the boat I compared that
the story of the Alter Rebbe and the boat, and that the fuel shortage in Ushuaia wasn't just coincidence, but was hachgocha protis.
Add in the Besht's maimor summarized below and a story of Rav Mendel Futerfas in Siberia and it was a powerful speech.