So I followed the example in the pathfinding2d demo linked in the question pretty closely, the only difference being I used hex tiles as opposed to squares. And the result I try to show in the image above with black arrows, is that the sprite literally only goes to the adjacent (horizontal) hex, one at a time. And there are only two points in the path, even when I want the sprite to go several hexes away (e.g. the red points I marked in the image).
And yes, I do want the path to go through one of the 6 directions of a hex. To be honest, I don't really know how navigation2d/navpolyinstance/getsimplepath works and wasn't sure if it would work with hexes in the same way it would work with squares in a tilemap. I think you're right it would probably be easier to script with AStar, I might give that a shot.