How about this? Uses Mesh Shadow to get the 2D projection before Sweep1.
vol_sweep_2018Apr8a.gh (11.7 KB)
Seems to work with a 3D curve as well:
P.S. NEVER MIND! It fails when most of the brep is hidden in the shadow…
P.P.S. In this specific case, you can connect the vertices of the oriented breps to get the enclosing volume, but it’s not a general solution that will work with all breps.
vol_sweep_2018Apr8b.gh (13.9 KB)
Ah, forget about it, it’s just a mess.