No matter where on the torso they are attached, I also have a problem trying to figure out how they fold up. They can't just open and close like a paper fan and still have a 7' wing spread- unless they attach near the top of the torso, below the gilled bulbous neck and then extend down to where the lower bulbous neck ends (see figure A, below).
Lovecraft's drawing and notes (above) confuse me because the sides of the torso have this jagged edge, like a pinecone or something. I think those are the wings folded up. On the left side, there is an arrow which points out to the note: (circled) "Fan-like expansible to 7 foot spread." And then: "veined ?????-membraned comb-????. At tips- ends of veins are spore cases." So, those could be the serrated edges of the comb-like wings somehow sticking out of the furrows, but....I don't see how those would unfold....unless the tubular veins extend each time, but I doubt it.
Go check out the full article. It's filled with beautiful illustrations, including some inventive motion studies.