Having a lazy day at the office, I gave this a try. It's a well known mathematical problem called "The Traveling Salesman". Unfortunately, I'm no mathematician and can only use my common sense.
"KBAP travel quest" is a breakdown of what Elwin wrote. I'm not sure I have all the quest items correct (1=start, 2=task, 3=collect reward, but not always). I think that the challenge of the Island and the location of the navigational charts are things to be taken into account here.
"KBAP travel time" is my solution to for least amount of travel time. It's 93 hours.
No fancy pictures, just excel. Feel free to comment and I will update. If someone can make better looking attachments, feel free to do so.
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