How do I animate the shrink/fatten value on a beveled curve?

Question

I have a twisted cylinder shape made with a beveled Nurbs Path, which needs to bulge and shrink at specific vertices over time (like how a person's Adam's apple moves when they swallow). I'd prefer not to convert it to a mesh unless absolutely necessary because the mesh would be way too high-poly to manage, and I'm going to make a lot of these shapes. And since I'm not at all experienced with Cycles, solutions within the internal render would be best, but I'm willing to learn how to do this on Cycles if there's no other way. So far, I've tried animating with Shape Keys but it doesn't seem to work on shrink/fatten (Alt S) or curve radius changes on individual vertices. Any help is appreciated!

Here's the .blend file

Answer 1

You could animate a Taper Curve, using shape-keys or hooks. but perhaps a more direct way would be to activate the Animall included Add-On.