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Off the top of my head, I would maybe try to break into quadrants or smaller, then do a circular pattern and combine.
Try a surface loft, discard your 'profile", and just loft from the inner circle to the outer "wavy". Then make your "start condition" "tangency to face". Are you concerned with the curvature where the surface ends at the wavy? If so you could create a "ruled surface" out from the wavy. Then I would suggest using a tangency to face on the inner and a curvature to face on the outer. I'll take a look at it tomorrow, there is probably an easier way than even that...
I had the same thought as Anna & Charles. I would model one section using a Boundary Surface and then pattern it using the Circular Pattern feature.
I threw together a quick example. The file is in SolidWorks 2008 format.