Ewan, thanks for your paper reference; very relevant.
You wrote there, "ITD dominance is shown indirectly in findings that head movements are
highly effective for localizing low-frequency targets but not
narrow-band high-frequency targets."
I agree. But it doesn't address what you could do with wide-band high-frequency targets. If the alarms used 3 kHz, but chopped on and off, with not such a high-Q resonance, they would probably have good enough onsets to help you make use of ITD, yes?
I often see people disregarding ITD as a powerful cue above 1 kHz or so; but the basis for that is only that it's not a usable cue for sine waves and other narrow-band signals. Wideband clicks and noises are easy to localize, even if simulated with only ITD.