Parametric Twist Facade

I am looking to create a series of twisting surfaces (for a building facade) that run along a curved surface. I want the twist origin to take place in the center of the surface and allow the center to twist a full 180 degrees. I've seen this done vertically via 90 degree parallel lines. However, i'm looking to do it horizontally to the surface in the image below. Is this possible? Help!

I am having a hard time figuring out how to divide a surface into even lines that travel from one in to the other and still follow my original surface curve

Thanks!

(I have attached an example photo, and the rhino file of my intended surface)