There was an extensive discussion about the map at Frog in a Well (http://www.froginawell.net/china/?p=75)--it seems that a committed group of Asianists are quite skeptical of the map's authenticity (that is, as a product of Chinese exploration.) Something that seems odd to me is that it does not have the typical orientation of Chinese cartography--this one bears the mark of a mentality of European exploration, even if it is centered on the Pacific. You're also right about the projection methods. Chinese used a rectangular method, very accurate for area maps, but nothing else. I'll bet that the map was copied from European sources, or was even a gift from a European power.