"Project" command does not show correct projection of Brep/Lofted Surfaces. Edges/Contour is missing!

Hello,
I want to create a line drawing of a boat hull design with different sections which are projected to the relative view. In adition the contour/silhouette of the hull should be projected as reference outline. See attached Screenshots of my goal. However the projection of the hull does not contain any “belly” curves, but still the correct “belly” (surface?) is displayed by grasshopper. I cannot find a way to extract the surface or surface-edges. Make2D command is pointless, as it automatically projects to XY Plane and list of curves is constantly changed after recomputing. See attached my Rhino Hull and projection aim.
Silhouettes command in rhino seems to get the job done, but I need it in grasshopper…

Thanks

Hull projection Fail.gh (5.9 KB) Hull Projection Fail.3dm (261.8 KB)


Hull projection Fail_re.gh (93.2 KB)

Thanks @HS_Kim for your quick and clever solution! However I found that it does not work for another hull I have and cannot find the problem in the hull itself (bad edges etc.).

Also I tried to avoid using Make2D as the projected image is not on the projection plane itself (the sections are projected to their relative belonging plane). To solve this problem I added reference Geometry for the Make2D command (One horizotal and vertical line) to later on find a matching point for a move command. The problem here is, that the index of the reference geometry in Make2D List ist different after every new computing, so I have to manually sort out the correct index everytime.

I think the best way to do it is by using the project command, but why do the lines not show on the projection?

Here is the other Hull geometry in case you want to take a look.Hull 02.3dm (681.8 KB)