Problem modelling this fan shaped vase

 From:  duke
2199.1 
Here I am again! It's not your average profile-and-lathe vase:

http://www.baccarat.com/en/home-decoration/decoration/vases/GINGKO-VASE/product/GINGKO-VASE-CLEAR-CRYSTAL-GRAND-.htm



http://www.dukecg.net/GinkoVase_01.3dm

I sketched out the curves and everything is in the right spot I think, so I selected a closed set of curves and did a network on them. My problem is 2 fold:

a) I have no control over how it interpolates it. You can see a weird lump happening on the corners in the top view.

b) I can't thicken the thing, via outline or extrude (although I know extrude is just directional, not along normals).

I suspect i'm just coming at this from the wrong direction, as though i'm poly modelling it. Any input is appreciated :)