I found a construction photo that shows that the main shape in question appears to be saddle-shaped:
This looks a lot like a hyperbolic paraboloid:
Using the UV_Polygen plugin with x = u, y = v, and z = u2 - v2 for -1 <= u <= 1 and -1 <= v <= 1:
Plugin: https://sites.google.com/site/spirixcode/code/uv_polygen.rb
Model: saddle.skp (184.6 KB)
(BTW, There’s a newer version of UV_Polygen available on GitHub, but I’m not sure of the current status)
[added] Model with thickness added: saddle2.skp (358.1 KB)