Hi Jean-Paul, yeah it was that slightly twisted profile (it was bending just a little bit in 3D rather than being a flat planar profile) that was making the surface offset not work right there.

I've attached a tuned-up version where I used Transform/Align to get all the curve control points to be on the world plane.

This version should now work for you, I've left the pieces cut up so you can now select these fragments, which are from trimming but leaving the pieces behind.

So you want to select those fragments:



Run Construct / Offset / Shell to thicken them all into solids:



Now select the outside surface of these new solid pieces:



And delete it to make that open, leaving a kind of cavity structure:



Use Edit/Join to join those cavities to the outer structure to make the final result:




But I did just a quick job with re-using the old projected curves that were projected on to the slightly twisted surface, you'll probably want to actually re-do the projection of those on to the fixed up surface instead, to make sure all the things are aligned well.

- Michael