I don’t have all the add-ons you have, but maybe this will help some. What I did was make a 2D surface from your boundary curves and then extrude them. The extrude direction is any normal to each surface, so I used EvalSrf to find the normal. Since all the surfaces are planar all normals point in the same direction, so I used the corner point UV = (0,0) as the input to EvalSrf.
Everything I did is at the lower right corner of the attached file.
iris dome with joints-bb1.gh (98.2 KB)