I would personally build out the Sonic Tonic as a pedal and then insert it into the channel of the mixer or go straight to the pedal from the guitar and output to amplifier. The effect will be good for both of the final mixed signals.
I would say the first version might work. I have the equivalent of Barry’s Tone TwEQ circuit installed in my semi-hollow guitar as a pre-amp for the piezo, although I’m using 2 jacks and a modified Paramix board to mix the signals on the floor. Note, my piezo pickup just doesn’t play well with some effects, so try it before you modify the guitar. Mojo is hard to predict.