Mind BLOWN! This is astonishing, regardless of climate change! I have a history degree and I've done a lot of my own research - for a while I was almost obsessed with studying merchant and colonial sea voyages of the 16th to 18th centuries. I've read some parts of the original copies of the works of Captain Cook and Joseph Banks, in libraries - they were using longitude effectively for the first time, in the 1780s, and... this just doesn't make sense! How could Antarctica have been mapped so relatively accurately at a time when ships could barely find their way across the Pacific Ocean, never mind make their way through pack ice! I'm reading this late at night, so I'll have to look into it further tomorrow.
If the maps really are authentic 16th century maps (not fakes or hoaxes) I might actually go for your second theory - ie, that humans may have been much more advanced than we think thousands of years ago. Maybe they were advanced in some ways - for example, maybe they had electricity, but maybe they also used different powers that we haven't recognised or discovered yet. I'm not a fan of the "ancient aliens" theories.
I've done a wee bit of research and have found this interesting article from the New York Times in 1984, which you may have already read. Just fascinating!