According to the fifth city wiki, cardinal's honey is a byproduct of red honey production. We see the shuttered palace hiding a crate of the stuff early in nemesis before we know what it is apparently (which is horrifying). I doubt it goes bad, so any cage garden likely has several hidden bathtub sized caches of god-killing nuclear waste. So while we need a large lake of the stuff for this timeline, it's really a matter of logistics and time, considerably less time if earlier cities were making red honey.

Come to think of it, this is probably in the tragedy procedure...