I should have been more clear, my apologies:
The multicurve 1/4 cone shape is the target surface, not the source geometry. That, and the connector edges and projection plane are their own groups, within the single support group. My source geometry is in a separate group, which i included in the png this time. Hopefully the image makes it more clear.
I've tried reorienting the projection plane and connector edges in different ways, and tried to change how the hidden geometry of the target surface is structured, with no luck still.
And if anyone's curious, the end goal is an ornate fan vault. This is based in Gothic architecture but I wanted to incorporate elements of eastern architecture as well. The 1/4 cone section will be rotated into a full cone, which will tessellated in a grid. The bottom of the cone is supported by a column. If i figure this out I'll post finished product perspectives!