We made a precision Eddy Current probe for Monel Steel 1mm thick 1cm diameter using 100kHZ, 200KHz centre tapped differential coil in contact with tube inside surface while probing for metallurgical defects, such as a change in wall thickness of <0.1mm or a pinhole of <<0.1mm.
With 0.5 to 2" the loops you make must be > thickness and use a frequency that has a skin depth>= sheet thickness.
In order to measure the anomaly we used a custom precision quadrature PLL to measure real and reactive impedance using a calibration mark to rotate the data whereby with the correct frequency the two different defects will be 90 deg apart. The resolution of our net vector impedance meter was around 10 ppm.
I did this in 1978, but remember all the details as if it were yesterday.
In your case you just want to measure thickness.
ABB I see now has a patent on this. They have discovered that the Eddy Current time response of a current pulse has 3 stages and the last stage is thickness.
So by analyzing the change in slopes by differentiation, one can disable the reset on an integrator at t2 and compute the integral for a duration of X us or until below the noise threshold and capture the distance reading.