Best mixer for quadrature FM demodulator
Given that your signal is already a logic level and fairly tame in frequency I would look no further than using an exclusive OR gate as the mixer. Originally Gilbert cells were designed as a solution to making an exor gate so it would be almost rude not to use a regular exor chip as it was originally intended.



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Make sure the 90 degrees signal from the tank is schmitt triggered back to a reasonable square wave and you should be set to run. Example for 455 kHz: -



Circuit from here

Functionally and performance wise all the options you state are going to be about the same but the exor is going to be more tolerant of any rogue amplitude modulation caused by the tank.