Recording with many microphones

[mshilarious]

The lower the mass of the diaphragm, the less delay in reproduction of transients. There are some cheap ribbon mics out there that would probably do very well in that regard.

The polar response would be a problem; I guess you could use a pair at each point, but I think the transformer would pretty much kill any hopes of ultrahigh frequency response.

You should note, however, that the error can be slightly greater than that, depending on the waveform of the signal and the detection threshold chosen.

Well that's the key, we don't know the waveform he is trying to detect. In fact we have so little detail on the experiment it's nearly futile. Actually, assuming that it is an ultrahigh frequency is almost a best-case scenario (although I don't know what threshold air is capable of transmitting ultrahigh frequencies), because a low frequency wave wouldn't have a fast enough rise time to be detected over noise anywhere close to 5usec. So I was assuming it was something like an explosion, something with lots of broadband energy really fast.

At this point it seems like the OP has abandoned all hope . . .