Curve geometry, possible to 'fade' bevel effect?

I made a nice smooth scroll from a curve and used another curve in the ‘Geometry’ box to give it a smooth tapered shape. I’d like to use the ‘bevel’ to give it a four sided star shape through the middle section. Using bevel start and end just starts and ends the effect suddenly. Is there a way to have it blend or merge smoothly with the round shape at either end? It would be nice to be able to ‘taper’ the ‘bevel’ curve.
Thanks a bunch…
…now, back to the snow shovel argh

Could you use shape-keys to keyframe your star into a circle?

Thanks for the suggestion. I read up on Shape-keys and watched some tutorials, but they all work on an entire object, I didn’t see a way to be selective about it and only use part of one shape (or object).
So far the only idea I have is to make two objects, one round and one star shaped. Then superimpose them and shrink the areas where I only want one shape. I’d finish it off with a shrink wrap modifier to retoplogize the object. I have many to do and am hoping there’s a quicker and more elegant solution.