I'm not sure I understand why you think it's the math of the surface that makes the problem.  As far as I can tell, it's a pretty basic issue that you'd see in any shape with a non-uniform width or height, even a planar triangle. 

It looks like your problem is very simple: you're changing your density with your width.  In real life, the density of the weave would never change, but the amount of it would.  The ribs would lead down and stop when they hit the edge.  So the middle might be as you'd have it now, but the the top and bottom would  have at least one more rib on either side.  Given the current spacing of ribs, of course.  Or, in the first design, the woven parts would stop when they hit the edge.  Just like you've got them doing horizontally in the second design.  As they followed a path in the z and y planes, they shouldn't have shifted in the x direction.

But maybe I'm missing something.