As PBlurp from the Thinking Particles toolset doesn't morph objects in a volumetric fashion and the Inheritance Effector doesn't have an option to inherit positions along a spline, I tried to built my own mix of PBlurp and the Inheritance Effector.
Here is me tinkering with what I came up with. As xpressopresets.net will have a relaunch soon, I am thinking about making this as a xpresso preset. It needs a little refinement for handling, but the basic effect is pretty much there.
I call it 3D Blurp :-)