If the foot is parallel to the feed dogs then I'm not sure what to say.
I also just ran into such a situation. My blue Dressmaker clone likes to twist the fabric too. Especially the bottom piece in a sandwitch. I've adjusted the foot / dog alignment till I'm as blue in the face as the machine is with no success. I've also switched feet and it didn't change anything.
So there must be another cause I've yet to discover.
I see a lot of old oil on your presser foot and shaft, try cleaning the foot and shaft till they are spotless and try again. I'm not sure that will change anything, but it can't hurt.
You might lower the feed dogs and then lower the foot to see if it sits flat on the needle plate. That might show something.
Yeah, I'm grabbing at straws.
Joe