Meandering back to the original question, at the risk of going slightly off topic, this is a fascinating story on its own:
https://www.bbc.com/news/science-environment-47192952
Shackleton's skipper, Frank Worsely, was a very skilled navigator and used a sextant and chronometer to calculate the precise co-ordinates of the Endurance sinking - 68°39'30.0" South and 52°26'30.0" West.
The time-frames are about the same (1915 vs 1900), but the required degree of navigational accuracy in polar exploration is much more than a passenger steamer of the same era. It probably still doesn't come close to the implied accuracy for the original story.