I don't like potentiometers for position, because they wear out, have noise, are mechanically challenging to get right, and don't cover a large part of the possible positions.
You can buy encoders and mount them to an arbitrary shaft. This is done all the time in industrial control systems. There are optical and magnetic encoders, and there are absolute and relative encoders. I'd suggest an absolute encoder, so that you don't have to "re-zero" your system each time you turn it on. You can get from some small number of counts per revolution (100, say) up to 16,000 counts per revolution. Obviously, the higher resolution systems are more delicate as well as more expensive.
Allegro makes some nice mid-price magnetic encoder ICs that give you an absolute position with 2000 or 4000 counts of precision. Circuits are about $10 in small quantities. That's just the circuits, though -- you have to mount a magnet and calibrate and drive it yourself. Or you can buy a ready-made integrated encoder with shaft and everything; just hook it up and it works. Expect to pay $50 - $500 each for such a device with reasonable performance and robustness.