<<<Or possibly stick a magnet to your apparatus and position the head from a tape deck close to, but not touching it, >>>
That won't do DC. Moving coil or moving magnets are all velocity systems. The faster the movement, the larger the output signal, and they have to be specially compensated for that if the application is audio.
Ever meet a Theremin?
http://en.wikipedia.org/wiki/Theremin
Those will create a sound signal against the position of your hand or other conductive object. The volume of the instrument is one paddle and the tone pitch the other. The system will transmit DC. If the output tone rises from 1000Hz to 2000Hz and stays there for example, that means an object has approached the pitch paddle and stopped moving. If the object never moves, the output tone will remain at 2000Hz or until something breaks or goes out of alignment. 2000Hz tone represents a DC level and designing pitch to DC converters isn't that complicated.
The usual Nyquist restrictions apply. The lowest pitch tone needs to be higher than 2.6 times the speed of the object. So 10 vibrations or position changes per second needs to be carried by output pitch tones no lower than 26Hz for any kind of accuracy. I'd go higher.
This design has the advantage that you can record the changing pitches as regular, standard audio signals in a WAV file and convert them into motion and position information whenever you want.
Koz