It would help if you describe your problems in a more detailed way.
What I got from your pm is that the simulation was flipped, that should be fixed in the attached version also the mesh creation works better without using the cluster provided by crane. You can flip the mesh direction with the boolean toogle, by that you flip folding direction. Try out the implemented OnPlaneGoal to fix border verticies to XY plane, best input it after achieving the desired folding state.
Yoshimura F_re2.gh (27.9 KB)
Regarding facbrication, I have no idea what you want to achieve and I don’t know much about crane so I can’t help with that.
If you want to achieve the first picture you posted. Well that picture is not a rigid foldable origami, it’s more like a tesselated barrel vault like Renzo Pianos sulfur extraction facility. You can see that because there is no folding in the triangles on the bottom border. You could replace these parts after the simulation with planar triangles or cut them out of the simulation process and insert them after or skip the whole simulation thing and tesselated the pattern on a surface.