> "Hmm , but the viewing angle of each LED changes as you move into the spiral ? maybe?"
This still implies a line of leds going down to the bottom or the mirror. You could use a spiral of the Adafruit Pixels, you would probably not notice that they were spirals not multiple circles, and you would effectivly then have individual LED control over a simple interface.
All these are really more complex variants of a kid's kaleidoscope and you coupld probably do the same just with mirrors? A lady I know did some photos of flowers and such like through a home made kaleidoscope type thing she made and they are great
@David re "you could have a fixed (but slightly moveable) mount on the back mirror at 9 o'clock. ...."
You've pretty much described a "kinematic mount" , laser physicists use them all over their optical benches. They have a ball bearing in the SW corner, a 1/4-40 leadscrew with a rounded end in the SE corner , and another in the NE corner. (The back of the mount has two slots and a flat face in the approriate corners) there is a spring in the middle of the three contact points to keep the mount loaded up against the three spherical points.
Max could re-purpose some of the little electric car-mirror actuators? Maybe some muscle wire? Piezo stack?