Okay, so I took the keyboard with me to work today. I have never used a multimeter, so I asked my hardware colleague for help. He did some measurements on it and concluded that the diode is not defective or the wrong way round. He suspects that I accidentally soldered two contacts together on the other side, but he wasn't sure himself. Unfortunately, he did the measurements rather quickly and I didn't take notes, so I don't know for sure what he measured. Maybe I'll have to do it again myself.
Regarding his theory: I just learned soldering during this build, so it's absolutely possible that I messed it up somewhere. But I know I did a rather thorough visual examination after soldering it and didn't see anything suspicious. Just taking a look isn't easily done: if I'm not mistaken, I would have to de-solder and take out all the switches, which (given my lack of experience) might introduce other potential failures if done wrong. I wouldn't even know how to do this properly; I guess I'd have to alternate with the soldering iron between both contacts of a switch to warm them at the 'same' time and then quickly pull the switch out?
What would you recommend?
Another option might be to re-program the QMK firmware so that it puts out a '1' whenever '1qaz' is pressed. But I don't know if that's possible, and it's certainly not the most elegant solution.