I usually pull them up until they stop flapping. They will flap even with the spine cut. The muscles in the legs do that even without a brain connection. Sympathetic nervous system?
The time to stop flapping seems to correlate with health and size of the bird.
The picture is from Stoey's Guide to raising chickens. If you look closely, the head is neck down(throat is on the ground) but the body is twisted as pulled up. It is like you said!
I do this and it works very well