Since the leak is right next to our server room, it made sense to punch out the soggy drywall and let the water fall into a trash barrel, rather than have it pool up and drain into the wall, and possibly collapse that ceiling at the wrong moment. I cut the holes with a flat file, as nobody had a keyhole saw handy. This was easy since soggy drywall has the consistency of pudding. There's more photos in the gallery, including partner in crime Matt Dharm up on the ladder.
The drywall is a total loss, soaked through as it is. It has to be replaced anyways, so there's no harm in punching the holes like we did. Fortunately, this is not the entry hallway to our offices anymore. :-)
[Edit 12:30 Wednesday] I get to work this morning to find a) the mess we'd made had been cleaned up (we have NO brooms or such around the office, the contract janitor service arrived last night unexpectedly;) b) the duct isn't dripping today, or if it is, it's doing so very slowly. I'm told we've had minor drip issues before, which would stop before the AC guy would come, who would insist nothing was wrong. We can't let him get away with that this time.