It occurred to me that a Mobius strip twists through space. However the depicted Klein bottles (except maybe the Lawson one) seem to discard this twist. I've created my own Klein 'strip' that derives directly from a Mobius strip.
You can find images at:
1. http://i57.tinypic.com/mcq3q0.png
2. http://i62.tinypic.com/j5dp4x.gif
3. http://i60.tinypic.com/raytqo.gif

The first one shows the Klein Strip in the classic mobius view.
The second one is an animation which shows how it directly derives from a Mobius strip.
The third one is an animation that depicts how the rotation steps along the Strip.
I hope that these will qualify as Klein shapes especially as they derive directly from a Mobius.