Extrude Surface along curve to Boundary Surface

Calling on the crew for some quickly needed uni assistance!
I’ve been trying for 1.5 hours now to extrude the surface of the left grey object, along a curve to the right grey object, to appear as though they’re joined. I’m having trouble getting the surface to rotate along the curve to abut the boundary surface, and meet it face to face - it’s following the curve without rotation and is intersecting the boundary surface at an angle. Am I using the wrong command? How else do I do this? Help! Thank you.
Rhino 6 Screenshot.pdf (595.1 KB)

Yes. Use Sweep1Rail or Sweep2Rail instead. You cannot sweep a surface, you will need to do this with the surface edges or curves as profiles.