Is there no information about surrounding surfaces at all? It the curves suggest to me a relatively simple and understandable underlying shape may be luring there some place.
Problem28 shows the final shape of the part. When I was thinking it needed to be done with a networksrf/sweep, I knew the surface would not be able to stretch all the way around the curve. There are parts that go on top and bottom of this (and some details that get added). Finale trim shape looks like this:
I am still having the problem in Problem28 though. High tolerance operations fail with this part/surface. For example, In problem 28, I extract a piece from the surface then try to add it back in. That fails.
When I wanted to make this image, I tried subtracting the final top piece and that failed. I ended up subtracting a simplified version of it instead for illustrative purposes.
When I try to insert a solid in the space where the black piece is shown (see above), I cannot get a boolean union to work (that’s why I tried seeing if the part I cut out would go back–and it does not).
Methinks, I need to do something while creating the path or afterwards to make it work here.