An update for anyone who cares: I've done so more "experimenting." Previously, I've always powered on my LPA-1 by turning on the receiver I'm using as a pre/pro, a Yamaha RX-V659 (plugged into a Belkin power conditioner), connected with a 12v trigger. That's what causes the lights to dim for up to a minute.
However, I've found that if I turn on the LPA-1 by itself, the lights will still dim, but only for a second or two. If I then wait a few seconds and turn on the 659, the lights will dim again, but again, only for a couple seconds at most. The same is true if I reverse the order and turn on the 659, wait a bit, and then turn on the LPA-1 manually -- two separate second-long dimmings, as opposed to the 30-60 second dimmings that occur when turned on together via the 12v trigger.
I'm not sure exactly what this means, but the fact that the receiver by itself can cause any dimming at all makes it seem pretty certain the fault lies with the apartment and not with the equipment.
Man, I can't wait to move.