I'm looking to create a continental map for one of the continents from my recently created World of Eldaron map. The continent in question is Auctoria. Since completing the world map I wrapped it to a sphere, which I'm going to assume to be completely accurate at this stage. The world is a sphere with a 25,000 mile circumference (just a touch larger than Earth). After wrapping the map to the sphere in Photoshop I've wound up with this:

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Name:	The World of Eldaron - Sphere.jpg 
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My main question at this stage: How can I take what I have now (the spherical map, the original .psd that includes the original continental outlines) and create a new rectangular map of the continent of Auctoria with as little distortion as possible? I realize that with a continent this size distortion is inevitable, I'd simply like to minimize the distortion as best as I can. Ideally this continental map will be used as the basis for all the regional maps I intend to make.

I have the following tools available to me:
Photoshop CS4
Illustrator
Any other free/open source tools that might be of use