Make all longitudes into "positive and negative clock numbers modulo Pi" using modular arithmetic, so that everything wraps around the dateline correctly. This will mean special changes for most layers, because different layers handle the dateline differently. Most will need to need a hard stop that gets only visually matched with the other side.
This may mean special stuff in the vector branch, e.g. what happens when some draws a line across the dateline? or drags a polygon across the dateline? or clicks in a feature that is on both sides of the dateline?
While it would be nice to also work out the code for pole crossing, it is more complex than just making latitudes into positive and negative clock numbers modulo Pi/2, because the singularity at the pole creates an orientation ambiguity that can only be remedied in one of two ways:
I think this means that pole crossing should wait for later.