I got it to work, but it wasn't easy. I ended up with a bunch of holes on the sides and bottom. I was able to patch them up using triangles then smoothing coplanars. There were a couple of line discontinuities, which obviously turned into a surface once I filled the gaps. But around the edges of the holes on the side there were no apparent discontinuities, and I zoomed in pretty close to find them. What else could have caused those?
I've attached the file for reference. You can try intersecting those two shapes to see what happens.