well, tiling managers automatically portion windows to fit the screen without overlapping. If you were to run something like awesome WM, or even fluxbox with pytyle, all you'd have to do is make an icon on the screen for changing between landscape and portrait. When it goes to landscape set the res to something like 1366x768 with xrandr, and when you hit the icon, have it run xrandr 768x1366, and then the screen will be in portrait mode. you can also set screen rotation in a similar fashion.