The winding issue shouldn't cause uneven lighting across the frame. You can expose film mechanically by stressing it severely (e.g folding) but that wouldn't cause what you've shown above.

It's entirely possible the shutter in those is like Trask describes and not what I was thinking off, which would mean you get no alternation of darkness from side-to-side in the case of a lazy shutter. Another experiment you can do is to shoot a correctly exposed blank wall at the three highest speeds. If the darkening gets progressively worse at highest speeds, you can be confident it's the shutter.