I was going to say, "what about a stepper motor"? or 2. One for the hours hand, one for the minutes. They wouldn't have to constantly run, but just update the positions of the hand about once per minute or so.
You won't find one that has one shaft inside the other like the hands of a clock, but you could take part of the gearing from an analog clock and figure out which gears need to turn by how much to get the hands where you want them. You might have to have a calibrate function where you manually push the hands both to midnight, then press calibrate so the controller know where they are to start.
They would not need to be powerful or fast, was thinking you could even make one. Or possibly use the idea of how they work and position magnet coils in the certain spots behind the face of the clock to get the same result that a stepper motor would get. Basically the position on the clock face farthest from where you want the hand to be would get a current flow to repulse the clock hand. The ones near it would get less. The ones 90 degrees from where you want it to be would get none. The coils closer would get some, but in the attracting polarity, and the coil directly under where you want the clock hand would get the most.
If you use permanent magnets in the hands, one could be close to the center post and the other could be way out at the tip. And so 2 rings of coils(total 24).
Or you could put coils in the hands, too, and only power the coil of the hand you want to move, so only 12 coils under the face of the clock.
You might be able to use a lot less coils. I know stepper motors have a lot more position than they have wires. I know they work by putting current through more than one winding at a time, but I'm not quite sure how they do it beyond that.
Maybe as an experiment you could start with 1 clock hand, a permanent magnet and 2 coils of wire and see if you can control the position manually by adjusting the current through the 2 coils and see how much current is needed.
Anyway, I was going to post all that, but when searching for "make your own stepper motor" someone's avatar picture was this:
Is that a "Gray Coded Wheel"? (or a section of one?) If that is, then I just find it funny that you mention them, and they I immediately come across a picture of one while searching for something else.
--tim