I tend to agree that we frequently would do better to make do with an atlas of charts rather than seeking the One True Map. But I'm not sure I like the differential geometry metaphor. It is not the location on the globe which makes use of one chart more fruitful than another. It is the question of scale, or as a computer nerd might express it, how zoomed in you are. And I would prefer to speak of different models rather than different maps.

For example, at one level of zoom, we see the universe as non-deterministic due to QM. Zoom out a bit and you have billiard-ball atoms in a Newtonian billiard room. Zoom out a bit more and find non-deterministic fluctuations. Out a bit more and you have deterministic chemical thermodynamics (unless you are dealing with a Brusselator or some such).

But I would go farther than this. I would also claim that we shouldn't imagine that these maps (as you zoom in) necessarily become better and better maps of the One True Territory. We should remain open to the idea that "It's maps (or models, or turtles) all the way down".