How to fill a closed spline with mesh

[FanManPro]

I'm looking for a way to fill a closed spline with a mesh. Most of the generator features seem to support doing mesh operations *along* a spline, but I cannot find features related to closed splines.

I got kinda close with a Input Spline Shape, but then I ran into issues with overlapping polygons that resulted in z-fighting.
   

And in other cases the inner vertices from one half of the mesh extended beyond the bounds of the opposite end.
   

The end result I'm looking for is something like this, where the red dots are the control points. (excuse quick hand drawing)
   

Thanks