As recommended my project is set to a 1:1 ratio resolution (720 by 720) to accommodate Portrait and Landscape mode. I keep the game's Screen and Buttons separate so that I can rearrange them based on device rotation. Both of them are children of the Game Control, which is anchored to the Center Top:
On all devices the Portrait mode works perfectly, and on some devices Landscape works fine. I don't even have to move the GreenScreen node, the program just centers it automatically on rotate. When it does work, the layout changes between these two images:
However on only some Android devices, when rotated to Landscape mode, everything gets screwed up. This happens instead:
This behavior persists even if I change the GreenScreen node into a Control and try to anchor it to the Center Top. How can I standardize the behavior to always center the screen on all devices? I think if I can at least get the GreenScreen node to always center itself no matter what the device is, then I can bet the other Controls to follow suit.