Surface from 3 perimeter curves?

This seems like an incredibly simple operation but I just can’t think of an easy way to do it. I’m looking to create an egg-shapred closed brep from three closed planar curves, each one defining one axis and containing the origin.

This example has them entirely symmetrical; going forward I would like to lose that constraint (but they will always be closed planar curves, on a world XY/XY/YZ plane, and contain the origin)

I’ve come up with various convoluted lofts and rotations + transforms, but they all feel wrong and overcomplicated and fragile. What am I missing?

lightegg2.gh (6.1 KB)

lightegg2_re.gh (11.0 KB)

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Thank you so much. I knew it had to be something straightforward. Rail revolution is the concept I was missing.

Also thanks for the wonderful expression of a domain as a text parameter. That will come in handy.