A couple of years ago I inadvertantly discovered a way of getting a PI to discriminate, AND IT WORKED!!!
If you look VERY closely at the dv/dt of the LOWER portion of the decay from the coil, then you'll see that it changes, one way for ferrous materials, and the other for NON ferrous.
Sampling this decay using a Digital scope, with a delay on the trigger, made the near vertical edge of the initial pulse, move one way or the other, depending on the nature of the target, i.e. iron or gold. this movement is VERY pronounced.
A nifty bit of circuitry to emulate this, would entail a delay in the signal path, but the trigger would be immediate.
Sample using a 14 bit A to D, store the results in RAM, then finally analyse using a micro.
You'll find that the depth this system will pick up a