This pickup is Zeta's own, albeit an early model that has since been superseded. The piezo crystals appear to integral to the bridge itself, because the wire runs out the bottom and into the body. BTW, I heard from someone who has the later version, and he does not have the thump problem.
I temporarily put a guitar sound-hole mag pup under the strings, and confirmed that there is no thump. My choices are to upgrade to the new bridge and electronics (not cheap to do) and hope that the thump goes away, or to add mag pups and mix it in to reduce the relative influence of the thump. Some thump is good, just not too much.