"Hi, Sim. Nice to meet you. You're my good friend!"

While I haven't noted this as scientifically as you, @MoonlightGraham, I have noticed for some time that using Cheerful Introductions dramatically and instantly boosts my sims' friendship level pretty high with any random stranger they use it on, so if I don't want that rando to linger in the relationship panel for too long, I make sure to use Friendly Introduction, which is much tamer.

I don't know that it has anything to do with traits or, if it does, how they influence/interact.