Snail Shell: Curved Line Following Spiral Spine, Help Please

Hello Adobe Community, 

I am trying to figure out a way to make this curved line follow a spiral in a uniformed way.  Using blend moded and replacing the spine, I was able to do it using circles but I don't need circles, I just need one arched line, perhaps going from one side of an oval going to one side of a cirlce in the midddle. See photos below to get a clearer idea of what I mean.  I am trying to make a snail shell and struggling through it. Any help or ideas would be greatly appreciated, thank you!! -Sarah 

PS: I was thinking if there was a way to choose where the spine was anchored to the blended object (the curved line), that might be a reasonable approach. Not sure if that's possible though.