I'd love to make the change, but I'm not using any physics in my game. If you notice in the .capx, it's all Solid and Platformer behavior.
Is there any other solution besides using Physics?
Collision polygon sqiddster refers to doesn't really have anything to do with physics behavior. What he means is, going to iamge editor for each object, and checking that their collision polygon (the icon at the bottom of toolbar) is what you want it to be. Your 'movingTileUpDown' has some funky going on with it's polygon.