Here is an out of the box idea.
Extrude your sketches at what ever angle you want the tangency of the surface to be. Use these edges to create the boundary surfaces. The benifit of this is that the sketch that determines the extrude angle can modify the puffyness of your umbrella. I hope this helps.
Try a boundary surface. The guide curves can be very simple, lines at ribs, and points in the middle of each bay that are on a plane slightly below the ribs. All of the ribs can be on the same sketch. All of the points in one sketch.