I was experimenting with some other possibilities other than sweeping.

Here is one totally different way - here I took just one rail and one cross-section and instead of sweep I did a rail revolve, with the curve that used to be the sweep rail as the revolve profile, and the one that used to be a sweep profile as the revolve rail, with the axis running down the pole.

Then I turned on surface control points and switched to the front view and tweaked them vertically until the profile matched up with your original spine curve pretty well.

- Michael