Map Curve to Surface Problem

I'm trying to map two "ZigZag" curves to 2 surfaces but I'm getting gaps between the mapped curve and the target surface. I've made sure that the source and target surface are untrimmed.

It is only the straight line section of the curves that have the big gaps... the rads in the corners map much closer.

Is this because the MapToSurface component is mapping the curve control points and then drawing a new curve through these, which takes a shortcut that deviates from the target surface?

Any idea how I can keep the curve exactly on the surface?