I would like to get rid of the header completely and allow the entire tile's area be grabbed and used for swapping? How would I approach this?
Only the header may be used to drag the item so one way might be to retemplate the TileHeaderPresenter and Tile elements. You could retemplate the Tile such that the TileHeaderPresenter will take up the entire area of the tile and host the Content within it. Then retemplate the TileHeaderPresenter to just have a ContentPresenter that will host the content. I've attached a basic sample that does this.