Splitting Curves at Intersection Points, Selecting bottom halves

I'm unsure of my underlying approach, but my end goal  is to split the catenary curves I've generated connecting from a central vertex point above an ellipse, to x division points located along the ellipse.

I'm trying to split them off at a certain height, to utilize the lower (or upper if I needed to) portions of the curves.

My end goal is to create a lofted catenoid-looking object, that fills the surface area represented by only the lower curve sections after splitting the original catenoid curves.

Any help, or ideas would be greatly appreciated!

Easily enough, I have achieved a solid difference operation which returned a brep for the section I'm interested in, but I realized I need to "surface" as opposed to a "brep" as grasshopper sees it, to utilize this generated figure the way I intend to.

Thanks, 

Zack