Mike that's one way of making it incredibly complicated.
All he needs to do is record a single synchronized timestamp of each peak signal event. Using an opamp as a bandpass in the interested frequency range to filter out as much garbage as possible just record each event that's over the volume detection threshold that's chosen. The hard part is the algorithm that does the triangulation, triangulating a signal location from that many possible points wouldn't be easy because not every microphone is guaranteed to have heard the shot, there's also echo's.