Hi Nick,
How about building your own FFD with falloff. The Mesh deformer could do the trick. This is just along your question.
Screen capture: one minute (please download it for a better viewing experience)
https://www.amazon.com/clouddrive/share/VuOL2gulnJdCBDI12gpazcybaGYMQJRRanukWzFAsVw
Another way would be with the Correction deformer. Update the deformer and then use the new points to create your shape. With teh Falloff enabled, you get the wanted change.
Screen capture: one minute
https://www.amazon.com/clouddrive/share/6ekXqEWQeFEv8SBorNJNKClR7az5rLgFQcyeywBZbfo
As the third option I would utilize the PoseMorph, to store the deformation. Which can be done with a FFD as well. Disable the FFD after ta pose is stored and the Pose Morph is set to Animate.
The PoseMorph deformer can now use the stored information and work with it along any falloff.
Screen capture: one minute
https://www.amazon.com/clouddrive/share/wDK1QgTjkLigkjPUEKSulO8SSa0HJpDjF21svDMeUlm
All files shown in the screen captures are in this zip-file:
https://www.amazon.com/clouddrive/share/5n4hSLGikf9id8K1zPj8Qpk3HbCAa8MhvcxpSFgU0ty
Let me know if there is anything else, I’m happy to look into it.
Cheers