Well, that picnic-table swarm (see below) stuck around for exactly one day. I got 'em on a Tuesday, and when I checked on Thursday the hive was empty. I'm wondering if they reacted badly to the comb I'd put in from one of my other "vanished" hives... maybe there's something in the comb they find repugnant?
At any rate, I charged $100 for this particular removal, so I still came out okay. One thing seems clear; there's never going to be a shortage of "bee calls!"