My persistent Debian-related WiFi problems finally got solved. The other day, I sat at a restaurant, working away, and decided to try the WiFi. The laptop connected, immediately, with no problems whatsoever.
This got me thinking.
Apparently, Debian and the Intel drivers couldn’t be to blame. It had to be a router issue. So I upgraded my Netgear router firmware (I have both a gateway and a repeater, so there were two machines to consider), and voilá! I had a working WiFi connection at home.