So Steve called yesterday, because it wasn't working. We went over a whole bunch of things, all of which he'd already tried. And then we shook our heads sadly.
Later, I sent him an e-mail suggesting that just maybe there was a detached ribbon cable inside the device, which would prevent the ADAT port from sending data through.
And tonight, Steve opened up the box and found the detached ribbon cable. It is now plugged back in and the ADAT port is working nicely.
And there was much rejoicing. :)