You don't *need* a 12x12 crosspoint switch. Six coils is twelve leads so you do need 12x something. However, with only six coils, any possible series combo (including any polarity combos) can be constructed with only seven nodes. Any time you parallel coils you save a node. That means you only need a 12x8 switch. That gives you a spare node, so you could take the output from the wiper of a pot connected across two nodes to permit live fine adjustment of the hum-bucking effect. I'm currently envisaging it as a 12x8 crosspoint switch powered by a 12V battery, e.g 4LR44, to get enough headroom as the battery discharges, a micropower OPAMP as a rail splitter to get symmetrical +/- rails for the switch with respect to output lead ground, and a ultra-low quiescent current regulator to power the MCU.