Core saturation detector-differentiator
I'm offering this answer as an alternative saturation detector. Pass a direct current thru the coil that can be varied from a milli amp to possibly several amps. This is easily achieved with an opamp and BJT as a constant current generator. 

Next, generate a low amplitude sinwave and capacitive couple it to the inductor. Measure or view the sine amplitude on an oscilloscope and, gradually raise the dc current. At some level of current the sine amplitude will begin to drop indicating the onset of saturation. More dc will mean less sine amplitude because of more saturation.

The sinwave can be sourced from a regular bench oscillator with 50 ohm or greater output impedance.

You could even incorporate the inductor into a colpitts oscillator and watch the frequency rise as saturation increases.

Looking at your formula, it seems that the centr frequency is \$\dfrac{1}{2\pi\sqrt{C1 C2 R1 R2}}\$ but I'm on an android and don't have full capabilities to analyse.

Thinking about it a bit more, because of the virtual earth nature of the circuit, R1 and C1 are independent of R2 and C2 so high pass is dictated only by the input components and low pass dictated by the feedback components. This of course assumes LP and HP frequencies are significantly different and by the sound of it they are.