Well, that guy's crazy-sounding "karate chopping" technique works like a charm every time on both guns. I was a little skeptical, but it works! You flip the take-down lever as usual, let the slide spring forward, then tap the back of the slide with the knife edge of your hand three times and it almost flies off.
I then took a look at the trigger assemblies I thought were broken. One definitely seems to be broken, but the other was just as he described - when I flip up the silver plate on the right and work the trigger connection, the hammer springs up just as it's supposed to do!
I'm going to have a go at disassembling, thoroughly cleaning and reassembling the other trigger assembly. I have a working model to go from.