What’s a good scroll bar equivalent for a spiral script?

One of my friends is writing a fictional story about a people who use a script that is read in a spiral from the inside out. They write on long coils of flexible material, and longer texts are fed into a mechanical device which feeds the coils into a spiral path. One can crank a handle to rotate the spiral and progress through the text.

Evidently, they are technologically advanced enough to have computers, and my friend wants me to help him figure out how their computers would work differently than our own. We've decided that they would probably use a circular screen instead of a rectangular one, and we've had lots of interesting ideas about how different user-interface metaphors would apply to them.

Anyway, we've had a hard time figuring out how page scrolling would work. That is, if there is more text than can be displayed on one screen, how should one scroll to see different parts of the text?

I have created a demo of text displayed in a spiral (in English, but imagine it in a script designed to be that way.) There is a horizontal slider at the top of the page that you can use to spin the spiral inward or outward. (Here's an animated demo, just for fun.)

The problem with this is that a horizontal (or vertical) scrollbar is a bad metaphor for a spiral text. I've thought of using a circular scrollbar around the spiral, but I'm not sure if that would be any better for usability.

I've also thought of clicking and dragging in a circular motion, counterclockwise to scroll the spiral inward, and clockwise to scroll it outward, but that doesn't give any indication of how far through the text you are, and I'm not sure if circular clicking and dragging is a good idea anyway.

How should spiral text be scrolled?