It would be interesting to see how well this could detect non incident sounds - for instance detecting reflective/resonant hotspots in an audio mixing/recording room.
I found that quite hard! Curious if there's anything public about your approach :)
With high enough frequencies I can see reflections, but not at any distance, and the sound source has to be loud. Of course, I'm relying on line of sight, and perfect reflection. Any bumps in the wall would add some phase error I think.
If I ever get a chance to work on the problem again I'd love to see if anything interesting can be done with multipath.