I don't know if this would work for scrappies, but when I made one, I sewed the first two strips together, pressed them and cut all my chimneys and first strip at the same time. (They are the same size.) Then I laid the next strip right side up on the machine, and put all those first squares onto it right side down and sewed them on. Press, trim and lay all those squares onto the next strip. Press, trim and do the next strip, etc.
Works slick, and the thing is square because it is squared up after each addition.