I don't think that would work, you would just end up with "howl back" due to the proximity of output signal to input
I didn't mean acoustic feedback: It was the proximity of the output signal going to the the piezo next to the pick up wires which could cause oscillation, like poor lead dress in a tube amplifier
Well if it's not some form of acoustic feedback it's still some type of physical feedback oscillating the string. With the coil method it's magnetic, my understanding is that the piezo is to vibrate the pickups field which will be that of the feedback frequency. The strings vibrating at 1,000 hz, you loop it back to the pickup by means of the piezo and capitalize on it's field.
I have to admit I haven't gotten around to building the one in the diagram I posted, I was taking it on faith that it worked due to the claims of others and the reputation of the sites I found it on. Honestly, I suspect an LM386 doesn't have enough juice to get the piezo oscillating intensely enough. I've experimented with piezos here and there, I can see how it should definitely work but not without at least 2-3 watts of RMS power driving it.
Maybe a dual op amp with one stage cascading into the other, both with a gain of 1000 and a +9- power supply?
I guess I'll get around to it over the next week and check back in so I'm not just blowing my own horn.