A circuit to find 3D position of an object using changes in magnetic fields
You could use three copper coils that are physically separated and have the user wear an iron or steel ring as you suggested.

As the ring moves nearer each coil the inductance will increase very slightly.  And as it moves away it would decrease.

You would need to characterize how much the inductance actually varies with position.  Unless the distance between the coil was small (say less than a few inches) my guess it that the inductance woudld vary by less than 1% of its initial value.  Which means that your detector circuit would need to be very sensitive.

To measure the inductance change you could run a square wave or sinewave through the inductor and a series resistor of known value.  Use a peak detector circuit to measure the peak inductor voltage.  The measured voltage should be approximately propotional to the inductor value when considering such small changes.

By recording the voltage measurements for various positions you could build a rough lookup table of value vs position (say 64 entries).  From the rough table you can determine position for any voltage readings by interpolating the table entries.

The capacitive sensor you linked is probably a lot easier since the human body makes a pretty good capacitor and therefore you can get a pretty good reading of the proximity to a plate.

This inductance to digital converter chip may also be useful.
LDC1612
http://www.ti.com/lit/ds/symlink/ldc1612-q1.pdf