Creating Compound Curves

I created this part using Revolved Boss/Base (Thin Feature):

(the model file is attached)

My question is if there is any way to construct (or approximate) this shape using SW's Sheet Metal tools?

Our layout guys could spend an hour or two to figure it out manually, but since we have the (CAD) tools, I'd like it to do the work for us. Any input is welcome!

SolidworksSheet Metal