There is definitely parallax in the first pic though. The optical axis seems reasonably well aligned (I.e. perpendicular to the dial) top to bottom, but the camera view point is off to the right. Just look at the apparent size of the left and right date window chamfer. The right chamfer appears more oblique and thus wider, the left more straight on and thus narrower. That also explains the date appearing mis-centered, and the original OP complaint. Of course it could be that the dial is not sitting straight in the watch, but at least these three observations are all consistent with parallax with respect to the dial in the original picture.
BTW, I own an Omega with what I believe to be a wedge-shaped crystal, so I am definitely sympathetic and open-minded towards observations of misalignment. But the picture in the first post is not sufficient as a diagnostic tool or as indication of misalignment.
I also agree with the warning that sending it in can make it worse. Happened to me with the Texas Richemont service center.
Good luck, and let's hope that Omega service is better than IWC service!