Here is that other method - for this I trimmed out the tightly curved section of your vertical curves and drew a tangent line there instead. Then I did a couple of 2 rail sweeps with the vertical curves as rails (with preserve tangent mode) to sort of bring down your top profile but have it conform to your curves.

But then this version ends in a plane - now the rounded parts come much more easily just by using fillet.

Does that do the trick? It seems to conform pretty well to your original sketch curves, probably the rounded area is slightly different. If you don't want a completely planar bottom floor to it, model a slightly curved floor as a separate surface and then boolean or trim it into place before doing the fillet.

- Michael