12-35mm Lumix ASPH for video -- strange jitter / OIS issue when mounted on a tripod

I am the original poster of the thread and the videos on Vimeo. You can find continuing discussion of this on DVXUser.

http://www.dvxuser.com/V6/showthread.php?302077-Strange-Panasonic-12-35mm-shakiness-possible-lemon-Any-others-see-this

And another example with the new lens here:

https://vimeo.com/59441889

I tested again with a new lens and I found that the problem persists. This issue largely won't affect users who use the lens handheld. For other users — still photographers who do long exposures, or video shooters who use tripods, I think this is a serious problem.

To underscore: the problem does not appear as much if the camera is level. But if the camera is titled at an angle, on a tripod, this effect will be noticeable -- sometimes at 100%, others only at 200 or 300%.

I viewed images through the camera's HDMI out to my SmallHD DP6 monitor in 1:1 mode and saw the jitters, so I am fairly certain that this is a problem in the lens/record chain, and not in the post-processing chain.