It seems I have been down this path before..
Just found a thread from 2009 with a similar problem of mine.
Guess I'm a slow learner.

The surface I'm looking for looks like this.
In that old thread Michael suggested using Patch in Rhino.

Hi renklint, here's a method by dividing it up into small 4 sided elements and then applying sub-d smoothing.



- Michael

Or you can use for this kind of task FreeCAD, that has the ability to make surfaces from edges, in this case the curves you provided and other three to close the contour.





To make it I've converted the curves in the Part Workbench into wire then I used those new to Make Face from edge, and it's done quickly but FreeCAD need a little effort to be used, in some cases can help.
Greetings

赞同，moi应该加入相应的patch工具。network,nsided，loft，sweep对褶皱曲率的曲线都处理的不好。（Agree, moi should add the corresponding patch tool. The effect of network, nsided, loft, and sweep on the curve of wrinkled curvature is not as good.）

In this particular case
You can make also a big surface by a simple revolve... with a generator curve as you want
Then trim them... maybe more elegant and easy construction! ;)