Does that other camera also have a APS-C sized sensor? If it has a smaller sensor, it may just not be seeing the problem that has been there all along.
The problem of the non-symmetrical vignetting may be just a de-centered optical train -- the camera's optical axis is displaced from the telescope's optical axis.
To check, rotate the camera angle without rotating anything else (i.e., make sure filter drawers, focuser, etc do not rotate). One way to do this is by adding a thin washer style spacer that is about 0.125 mm to 0.25 mm thick. The ASI2600's thread pitch is 0.75mm, so a 0.25mm spacer will give you 120º worth of camera rotation.
If the light and dark areas shifts when the camera is rotated, your problem is elsewhere in your optical train. It the light and dark areas stay at the same location on the sensor, it is a bad camera.