Found the bit and installed it (I took it apart and cleaned it after this picture and then threaded it all the way in). The stock shifters even seem to work okay!
Having three sets of cable braze-ons on the top tube and random bits of housing everywhere is a big change from what I'm used to. I think I got the cable positions right with a derailleur cable on each outer braze-on, and the rear brake in the middle.