I feel like I've been talking about myself overmuch recently, but I can't resist mentioning that my replacement wireless card came in the mail today! I installed it this evening, and so far it works perfectly.
It turns out all those hours of playing with Legos came in handy: there are two little wires connecting the wireless card to the antenna in the frame, which connect using a snap-on and off interface. As I was snapping them on, I briefly wondered how much force would be required to break them, which was followed almost immediately by the discomfiting thought that it probably isn't much more than the force required to snap them on. Thankfully, everything went without a hitch, and I am now enjoying wireless freedom again.