Thanks to my colleague at the NY Map Society, John Woram, the map pictured above was published in 1678. He notes that Tierra del Fuego is labelled Magellanica, meaning that it was created from sources post 1520.
Your "Mission Impossible, if you choose to accept it", is to find Juan Fernandez Islands discovered in 1574 and Diego Ramirez. found in 1619. If anyone can find the button for Enlarging the Image, send me an email!