I was puzzling about the first test I did on your circuit with the Diode incorrect. The square wave seemed to show only the 'bottom part of the wave', at the D pin, but there must have been some 12V part of the wave, for the COIL to 'see' How does this small 'top part of the wave' signal give a signal?
Without the diode the voltage due to the inductance of the wire makes the voltage go very high (few hundred volts) until the FET breaks down. There is still the same current flowing in the wire it's just not good for the FET. (see picture)
I have never tried the short WIRE on your circuit, as it would be too short. I have tried a medium 6ohm WIRE (Sorry to confuse) this showed a strong enough to use, signal at the COIL.
How high is it. This might be a good data point.
I think that if this is the strongest we can get with a 12V Battery, I will have to try other ideas.
I think we need some data and some ideas. Maybe you could make a plot of the coil output, the FET amplifier and detector output vs. distance. Then decide what range is required. We should also address how you plan to change the gain to keep the amplifiers from "clipping" once the input is high enough with the coil far away from the wire.
Is there something you can do with the micro to get the coil in range?
What would happen if I wound a Transformer to give more Volt, less Amps?
I think with a transformer we would need a different driver as this one has a DC component that the transformer wouldn't like.
The output with the long wire should have been 4X the 555 circuit with the short wire.