From my perspective, the basic problem is displaying a flat map (i.e. one that is useful for navigation or indicating points of interest) in such a way that it lets the viewer really feel the impact of the unique geography of the location. (i.e. that they are on the inside of a huge cylinder)

Simply unrolling the cylinder (as in image 2) gives a precise map that is useful for navigation but it lacks the gut-level impact that I hope can be communicated.

The same goes for image 3 which is a more artistic presentation of image 2.

One solution would be to present the map much as image 2 or 3, but provide a context image with the map (the maps projected onto a cylinder as you did) to let the viewer get the context of the flat maps presented.

I was just hoping to find something that could simultaneously present the map in a relatively flat way that lends itself to use for navigation at the same time presents those flat maps in such a way as to retain the impact of the unique organization of the geography. (i.e. That you can see the other "continents" floating in the sky above you.)