But how to measure this? The LCOS displays were buried deep inside some optics, and the only light that reached them was the laser light which was pulsing at the same frequency as the signal I wanted to measure, and the laser PSU was incapable of driving it faster. I did however have an pulsed energy meter, which I'd managed to interface to a computer so I got a readout for every pulse.
Sudden insight: flip the switch on the laser power supply from "Ext. trigger" to "Internal trigger". Twiddle the fine adjustment on the PSU frequency knob until the laser frequency was 29.95Hz. Watch in satisfaction as the energy meter described a neat sine wave over the course of 20 seconds - the beat frequency between 30Hz and 29.95Hz - confirming that the reflected energy swung wildly depending on the relative phase.
It was a small and simple hack, and I've poured much more sweat into much grander "hacks", but I will always be proud of that lightbulb moment.