Jon,
I cached it; hence, the changes (Spline) will not show.
I can’t see any foldings of any papers. The Soft-Body option is off, where would anything like the folding come from? Please let me know, I’m not sure what I have missed.
The Matrix is used here to get the data. If a Cloner is set up with a Dynamic, the Dynamic takes over. With Matrix introduce after the Dynamics, the information is available again for MoGraph.
You also wrote that you have tried all Damping values. So, I did not suggest anything. Let me do it now, set Dampening for Position and Rotation with a keyframe around frame 150 as is now, then at frame 160 to 123%. It stops right there.
I tried to give you an alternative option with the “Position Memory”, perhaps you give dampening another try.
If tweaking with a client on your side is critical, I suggest animating without dynamics. Furthermore, I would use several PoseMorph animations to have the folding, or bending, ready to go. Dynamics and clients might go well together, given that the time is limited.
Cheers