TheUser1 I agree with this, I think the whole idea of a kanban view is synonymous with having the groups be vertical (do a kagi image search for kanban view and compare the results vertical vs horizontal).
I am a horizontal tab view user, because I prefer the extra horizontal real estate whilst browsing the web. With that being said I much prefer the vertical layout of kanban prototypes in this thread, I personally think they look a lot better visually, whilst also providing better performance as they appear less cluttered.
I think implementing some form of button to take you to this kanban view (or by replacing the current tab overview), should take you into a vertically laid out kanban view, no matter your tab orientation.