alternatives to TOA and Phase Diff. for very rough sound localization?

I've been working on a small project where I have 6 of these Sparkfun LMV324 based sound detectors in a circle with about a 9 inch diameter. The intention is to figure out which side of the circle the noise is coming from, the ultimate intent is to just figure out roughly which 60 degree arc contains a person talking. The sound detector has a Gate pin wired through a Schmitt trigger and then the LMV324 that does a pretty nice job of setting a threshold for sound detection. I've done some Time Of Arrival by wiring up each Gate pin to an interrupt on a Teensy 3.1 and this does what I need it to do in a very quiet room but in a slightly louder room (i.e. with echoes and air conditioning noise) it falls apart quickly. I get lots of false positives until I turn the gain down far enough that it requires yelling to actually trigger the mic, so that doesn't quite work.

Reading through some posts on sound localization on this forum everyone seems to be pointing to Phase Differencing and while that seems awesome for fairly precise localization with sampling, I can't really fit a motor into a project and don't need anything as precise as Phase Diff seems to offer.

Is there an alternative to simple Time Of Arrival or Phase Differencing that's doable on an Arduino that I just haven't been able to google up yet? Any links or suggestions much appreciated.

the ultimate intent is to just figure out roughly which 60 degree arc contains a person talking

A common approach is to use a correlator, which would involve sampling each microphone separately and simultaneously, and then correlate the data streams to find the time shift at each microphone. See this overview on leak noise correlation: Leak noise correlator - Wikipedia

Not something an Arduino can do.

Ok, well that is definitely informative albeit not particularly encouraging :)

This is just for an experience demo and so doesn't need to be all that robust I guess I'm going to just hack around with some hardware filters and software based weighting to see if I can get it to be "good enough" to seem like it's working for the 10 minutes or so that's needed.