Barbara, I'm just working on these. The Flying Geese blocks (paper pieced) turned out really nice after several sessions with my friend Jack, but I kept learning, and it got better by the time I was on the 4th or 5th strip. Anyway, I think you flipping the strips in opposite directions is a great idea - haven't sewn those seams yet but I think the cross seams will nest better. Another thing I thought of, if I had realized it, would be to have one set of the strips pressed 'upwards' while paper piecing, and the other strips flipped down and pressed, which would make them nest - and have both strips facing the same direction.
Having fun anyway. Will post pictures soon.
Primrose