Short version: I've chickened out, a bit. Long version?
To make some sort of procedural "anything", you have to have an idea of what the building blocks of that "anything" are, or at least what you'll argue they are -- and then either frame your game in those terms or expressly simulate those terms. So if Convo is a game about narrative instead of people, then what's a unit of narrative?
From there, my thinking goes like this...
(DISCLAIMER: The following is a flawed stance on "how all narrative works", one that I probably wouldn't defend critically, but I've found it useful for making this kind of game with this kind of narrative. I think designers are not their games; you can make a slow artsy first person experience one day, then make a loud masocore platformer the next day.)
Fictional characters aren't people, so don't even try simulating NPCs like actual people -- don't model complex moods, nuanced personalities, or deep emotions. These supposed "relationships" exist only to force decisions to be made, and the heroes either get what they want (comedy with a wedding) or lose a lot (tragedy with a bloodbath). It's a mistake to project more than a sliver of humanity on a fictional construct. Let the player make that mistake, of empathy, but we the designers will know better.
All characters are fundamentally flat because a character is always just an idea expressed in a fiction, not a person. So a character is just a tool to generate plot. Plot and action are exciting. (In contrast, characters talking about their feelings is boring because nothing is happening.) So now, we can abstract away from the myth of psychological realism towards a cynical scriptwriter mentality: conversations are ways for characters to exchange information to make plot possible.
Juliet told the Nurse to tell the Friar to tell Romeo about X, but the Friar is too late. Someone else only tells Romeo X(0.5). Juliet thinks Romeo knows X.
But being a writer is boring, and that framing doesn't offer any intuitive goals to players: write the "funnest" narrative to win? How do you quantify that? What's the best plot, or a good narrative?
If you ever want to lose an hour of your life, you should read about the extensive Allied spy operations during World War II. Dozens of different operatives, double agents, and close calls. Spy thrillers literally commodify plot information as "intel" in a briefcase or flash drive that gets guarded, stolen, lost, destroyed, or modified.
Juliet told the Nurse to tell the Friar to tell Romeo about X, but the Friar tells Romeo about Y, luring him into a trap; when the Nurse talks to Romeo about X and he tells the Nurse about Y, then the Nurse knows the Friar told Romeo Y instead. The Friar doesn't know that the Nurse knows he told Romeo Y.
So, I think the "WW2 spy" concept helps emphasize information as a tactical object and provides game objectives under the guise of history / war. The game is quickly designing itself in this regard: war games are about what you do to win a war, and what you do is to collect intel and control access to that intel.
"Intel" isn't just the location of an 88mm Flak; it's also whether he was actually at the office when he said he was.
There's also a notion of trust, I think, that's relatively unique to a spy narrative, and is also very pertinent to a romance. Do you trust where you got this information? What if someone lied to you? What if you lie to someone else? Will you remember the lie you told and keep track of everything? Is it better to never lie?
And to lean on a cliche and tired rom-com tagline: love is war.