I'm trying to create a very specific part and I have no idea how to proceed.

I need a shape that is a 2:1 aspect ratio ellipse extruded in the +x direction, but whose semi-minor axis is given by the equation y=Sqrt(x).  Because the cross section is an ellipse instead of a circle, I can't simply revolve the curve given by the equation.  I know I can't do this directly with the extrude tool, and so I've tried lofting the xy and xy faces of the part using the ellipse cross sections as guide curves, but unfortunately this didn't keep the cross sections constant as 2:1 ellipses.

This part has to be extremely precise, and it seems that the loft tool's "best guess" as to how to create the surface isn't accurate enough.  I also considered simply making the part from a point cloud generated in MATLAB, but I can't figure out a way to do that without SolidWorks Premium (I only have proffessional.)

Does anyone have any idea how I can make this part?