I assume that these shipping routes aren't equidistant. This is, I assume that, if we trace a route at equal lengths, it wouldn't correspond to equal travel distances across the Earth's surface.
Specifically, the projection should:
Maintain equidistance along arbitrarily drawn routes.
Seek to minimally distort the other parts of the map, especially those closest to the routes.
Since such a projection would depend on the routes selected, it'd need to be more of a dynamic projection where the map of Earth looks different depending on the routes being displayed.
Question: Is there an algorithm that creates projected maps in which a selection of routes maintains equidistance?