"""""""Hi, BurrMan. Is your method different from the approach Phiro suggested? Does "its base curve" refer to the red profile?"""""""

Yes. I finally got a chance to download your file and found a small anomoly in one of the original surfacves, so I made a quick vid of me fixing it, but I didnt get into depth. Just showing a quick fix when a solid had "Naked Edges"

The area at the "red profile" on your zig surface had a couple little sliver surfaces that prevented it from becoming a solid (You see it in the video)

As a quick fix I just deleted all those planar surfaces and ran Planar which replaced everything. If you started by running "sperate" and just deleting single surfaces, you will see the little sliver.

Anyway, just for you to view what I did to your model to generate the bottom half you were looking for...