You're right in that the KPA isn't designed for this way of working, but in theory it is perfectly possible with its existing feature set, it's just that the feature doesn't quite work as it should.
It's not about having a stereo section; that part of the original post is misleading. The guitar's output goes into a stereo jack, which is split into two mono jacks, one carrying the magnetic pickup signal, the other the piezo. From here it's only mono. The magnetic signal goes into the KPA as normal, the signal flowing through the stomps, then the stack, then the effects slots (X & Mod), the delay and reverb, and then out. The piezo signal joins the flow at either X or Mod, as the return in a Mono Loop stomp effect (note we're not sending any of the main signal through the loop). Setting the mix of this to 50% should mix the main signal path (the magnetic pickup) equally with the loop return (the piezo pickup), and then the player is free to select which signal plays by simply using the pickup selector on the guitar. Sounds great, right? The only problem being, the stack affects the Mono Loop stomp signal which is placed AFTER the stack section, meaning it shouldn't have any influence over it at all. Unfortunately with the stack engaged, it gives the effect of the piezo signal going through a guitar cab, attenuating the highs above 5-6K Hz, losing a lot of the acoustic-sounding properties.
Cheers,
Sam