How would I go about easily implementing diagonal pixel movement?
I'm not sure what you mean. If you press up and right, your mob will move diagonally. If you want to make a single key that causes you to move diagonally you'd have to override the action() proc. You can either make it call the move() proc twice (ex: to move northeast call move(NORTH) and move(EAST)), or you can override move() to make it support diagonal directions.
Unless you're referring to diagonal movement in a different sense?