I am working on generating watertight unstructured splines in Rhino. There are occasions where such unstructured layouts need to be represented by surface patches in which edges or vertices of the same patch are identified with each other. For example, to rebuild a trimmed annulus as a set of unstructured splines with an single extraordinary point of valence 3 and a single extraordinary point of valence 5, one would expect the following layout (where boundaries of each of the 6 necessary surface patches are depicted in green).
I would like to use existing Rhino functionality (e.g. the rebuild function for boundaries and a sweep or Coons patch interpolation) to create these splines from a dense polyline. However, I face two problems:

The rebuild command makes my closed curves periodic. This means that the location of my extraordinary point may not lie exactly on the curve from which it was built (particularly for evendegree polynomial splines), which is absolutely essential. Is there a way that a curvefitting can be prescribed in which a closed curve must be interpolatory (clamped) at start and end points?

Rhino offers the sweep with two rails command to generate a single surface patch from two closed boundary curves. Alternatively, the _EdgeSrf command can be used to generate a Coonspatch surface from multiple open curves. However, there does not seem to be any functionality that will rebuild a spline from a (creased) closed curve and an open curve. This means that I cannot find a builtin tool from Rhino to generate the middle surface patch of this annulus (bounded by a closed looop and an open curve). The only alternative I can think of is to split closed curves into a composition of two open curves, but this would unnecessarily increase the complexity of the spline layout.
Does Rhino have tools through which the above unstructured spline layout can be generated (particularly with regards to the two above issues)? Thanks.