I think that the purpose of the map should be an important indicator of how to lay it out. For example if navigating one of the land masses, it seems difficult to move onto one of the other strips so a square map of one strip at a time seems reasonable. The artists impressions at top of thread seem to indicate that there is an attempt to keep them basically flat even though they span 60 degrees of chord.

The space is inherently 3D so I think a 3D viewing solution is required. Our earth is a globe but were not interested in anything other than its surface which is 2D. If applying the same logic then three square strips is the way to show it but thats bound to lack the 3D nature of it just like mercators etc lack the global feel of the earth maps.

If you did go for three strips then it seem logical that one of them should be much higher than the other two. The high res one being the one your stood on. Since the other two are less important from that proximity.

Id also like to chime in and say that if your not going to print the map on fixed sized paper then wasted space is of no issue.

I still think the fundamental question here is "What is the main purpose of the map", "What information is it meant to convey".