Yes, the variation you are seeing are caused by breaking the ribbon, basically. When you rotate the coordinates internally inside the cell, it doesn't "fit" anymore in the cell, it's no longer a properly periodic structure.
If you want to change the orientation of the ribbon, you must rotate the unit cell too.
However, again, this doesn't change the band structure, except of course is you keep using the point Z, which corresponds to different a point in the rotated Brillouin zone compared to the original one.
I suggest you think a bit more carefully about what you are actually trying to achieve