(1) → your geometry is far away from origin - any reason for this ? you should model close to world 0,0,0
(2) → your curves are polylines with a few hundred segments - you should use proper degree 3 or degree 5 nurbs curves to get a nice surface.
(3) your file is version 5 … there are huge improvements to latest version 7
not sure if I understand all your requirements / needs / conditions.
the curves do not form 100% rectangular / 90 degree relationship where it is maybe expected. Also what-ever you want to do as next step - it is a bit depended whether you focus on accuracy or curve / surface continuity, or on simple CV-structure / untrimmed edges for next step. …whether you need data for production or visualisation…
a simple workflow might look like this:
(1) construct a center-Line with tweenCurves (allready here you ll see some problems with the input curves - I used option none) (cyan at z=0)
(2) meassure the _length (you might want to increase the amount of digits displayed with preferences units (not the tolerance !)
(3) extrude the curve _extrudeCrv end enter “your length”/12.0 … for extrusion length (green)
(4a) draw a shortpath from upper left to lower right (red)
(4b) do some alternative workflow with _unrollSrf, _createUVCrvs, _flow…, applyCrv…
(5) _fin (in the file, not in the screenshot, white)
(6) _extendSrf (blue, transparent)
(7) _trim in top view (violett)
not sure if those parallel lines should be horizontal - if yes apply the workflow above for each section - but check proper curve set-up (90-degree, curve ends match outer curves…)