Mobius Catenary Arch

I'm trying to develop a grasshopper script to generate a 2d surface following a mobius twist along a catenary arch.
I've illustrated the desired effect in sketchup below:

I'm relatively inexperienced with grasshopper, but so far I've managed to combine the following:

Giulio Piacentino's "Catenary arch from height" script

Pirouz Nourian's "Mobius" script (Obtained from a friend)

End Result:

Here's where I'm stuck: I want the mobius twist to revolve around the midpoint of the arch, but the script uses the input values to determine the endpoints, resulting in a weird sinuous shape when viewed from above.
Also, the secondary end points (generated by the mobius script, determining the width of the surface) are generated by default along the z axis, resulting in an arch that only touches the "ground" at two points. I attempted to work around this issue by trying to force the zHeight parameter to correspond with the y axis (thus rotating the arch 90 degrees so it would lay "flat"), but the script interprets the third point as a value and not as an actual point to bisect.
I thought this might be an issue with the C# component that I obtained from Giulio Piacentino's script, so I attempted to tinker around with the source code. Unfortunately, I'm not fluent in C# so I only managed to mess everything up (I've since recovered the code from the cache).

Anybody got some ideas?
-BC