"I don't quite think of this process as "storytelling", which I envision as a somewhat more verbally-improvised art."

I almost never improvise, and fail more often than not when I try. I have a moderate amount of material which I tell in a semi-structured fashion, but the vast majority of my repertoire is word-for-word memorized. When I am preparing for particularly special performances, I even work on getting specific tones and gestures memorized. I did well enough that people called me a Master Storyteller, so I presume what I did qualifies as storytelling :)