"It makes no sense at all to me that your Sigma lens could vignette for video."
Well all I can tell you is that is does. I was shooting in standard 16:9 on a Panasonic G6 (Did the same on a GH3). No hood, not even a UV filter. As I said even wide open there is some shading in the corners, stills and video. I don't have any other DX lenses to compare, as everything else I'm using are 35mm lenses so I can't tell if its just this lens (this example or the model in general.) No problems with any other lens. Basically I really don't have any answers for you.
Personally, its not a