Möbius-like Surface?

Twisted Strip 2.3dm (3.3 MB)

Create closed curve in 2D
Move control points to expand curve to 3D
Create initial cross section normal to the the curve
Sweep1 using the 3D curve and initial cross section to obtain an initial surface
ExtractIsocurve to extract additional cross sections
The initial surface is only used as the source of the additional cross sections.
Line Tangent Point OnCurve for line segments tangent to curve at each cross section
These line segments will be used as the rotation axis for the cross sections
Rotate3D the cross sections as desired
Sweep1 using the 3D curve and the cross sections
Closed sweep. If Sweep1 fails because the cross sections cannot be ordered then manually select the individual cross section curves in the appropriate order.

Because it is a mobius-like surface, indeed splitting the middle with any rhino command would result in a double splitting. So first remove a segment of the loop, breaking it apart, becoming a open stripe.
Add the center line, and then recreate the segment.