I believe you are missing something.
While you are correct in your observation that the Piri Reis Map is from the middle ages (1513 CE to be exact,) the assumption that Piri Reis was actually responsible for charting the map is erroneous.
Piri Reis was an Admiral in the Turkish Navy in the Ottoman Turk empire, with a passion for collecting and redrawing maps. He traveled widely, and combined and re-drew ancient maps. This map of his was rediscovered in 1929, drawn on a rolled up piece of gazelle-skin. His own handwriting on this map states that he did not chart these waters, but redrew and compiled this map from ancient source maps he found.
What is remarkable about this map, is that it shows Antarctica, the continent “discovered” in 1818 AD, 300 years after his death. In addition, the coastline of Antarctica was completely “wrong” in his map – until in 1949 a seismic survey of Antarctica was completed. The Piri Reis Map shows the Coastline of Antarctica -- Under the Ice Cap!!!
The LATEST time Antarctica could have been ice-free is 4000 BCE. The Earliest – we do not know. The Source Map that Piri Reis used was obviously at least that old. And someone was skillful enough a cartographer to map Antarctica, in 4000 BC.
I believe that was well before the time of Plato. Plato also had access to the best resources of the ancient world, over 2000 years before Piri Reis.
I rest my case…