Happy New Year to everyone following this thread!

There has been some progress lately, thanks to the free time afforded by the holidays, so I decided to post an update.
I think I have found the best way to spin that HDD motor! The solution was there all along, I just put it off thinking that others may be easier to implement. The practice, however, showed that quite the opposite was the case. I decided to use the dedicated sensorless BLDC controller chip that was right there on the PCB of one of the HDDs which I broke apart to get the motor. It was a slightly older, circa mid-late 90s Quantum (I think) HDD, and the IC Philips TDA5143T was right on its controller PCB, free for the taking. I actually almost thrown it away, I'm glad I decided to look at the PCB second time before throwing it away.
TDA5143T (see attached photos) is a 20-pin SOIC IC. It is very easy to handle because SOIC, although surface mount, is still large enough of a footprint to easily use soldering iron on. I just happened to have a 20-pin SOIC-to-DIP adapter, so I guess you might want to get one if you are using TDA5143T - will make breadboarding easy.
It is very easy to control, only 4 external parts needed - the small ceramic or poly capacitors, value of which defines the RPM and the length of the spin-up period. It starts extremely reliably using its own built-in algorithm and works all the way down to approx 3.5V - important for me because I want to power the entire device from a 5V adapter. Using a 2.5" laptop HDD drive motor you can see on the picture draws about 150mA @ 5W - perhaps it could even be possible to power from USB?
So, anyway, now that I think I got the spinning part of the project done, I got encouraged and created myself yet another 3D model of the mirror holder, this time with surfaces at 1/10° to each other (0.25° surfaces created lines too far apart on the wall 10 feet away). As usual, the model is available from Shapeways here :
https://www.shapeways.com/model/1605919I will continue working on the project as soon as my new mirror holder arrives.