To paint outside of the game area, you simply provide the right coordinates to the draw functions.
For example, for drawing a tile on the left border, give a negative horizontal coordinate.
You can use four tiles, for left, right, top and bottom borders,
to avoid having a bigger menu tile (256x256 pixels may be a hardware limitation on old video cards).
For better performance, try to optimize your code in the draw handler.
For more info, read The Hud chapter from the DizzyAGE book.
