This is a fairly simple problem made hard by communication here.
the values you chose resonate at 2.91 kHz (1uH 7 mF)
maybe you meant microFarad (7uF !!) in which case that makes more sense 60.1kHz
The impedance Zo at resonance is 500mΩ.
Q= Ratio of Zo/Rs ( including coil) = resonance factor and for Q= 1, 10, 100, Rs= 500mΩ, 50mΩ, 5mΩ ( perhaps the coil Resistance) which results in a step response of <1 , 5 and 50 cycles
You will need 50 cycles for < 1% accuracy unless very precise threshold adjustment on counter.
This also means your connections must use braided wire or Litz wire or be very short.
Once way is to use direct COAX connection to an amplified shunt R of 5mΩ directly across coax and terminated by counter and scope.
Since this now means 5 mV/'per Amp, you can now choose your voltage and amplifier gain at 150KHz BW
I might suggest a pulse circuit that shorts out the coil after energizing it, however the counter AC couple may not response quickly enough and DC couple will saturate counter front end with battery voltage.
1st answer this
What accuracy do you need?
Using the pulse method is not low current.
Using my method with swept F is low current with gain on signal input from shunt in CD4046
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