I've got the base of the conversation system down now, thanks to Dan Cox. The idea I was going for was to keep a person in the same passage (aka room) while they speak so as not to break the illusion. Jumping to new passages in Twine creates small refreshes that I think break the immersion. Luckily there's a way to display the contents of a one passage in another.
[Here is some content]<name|(click: ?name)[ (replace: ?name)[ (display: "Passage 2") ] ]
So the text displayed "Here is some content" is replaced by the contents of "Passage 2". This should allow me to represent livestreaming better in what is effectively a text adventure, as all of the text is immediately displayed. It also allows for a passage to hold choices that provide further branching.
I'm not planning on having any sort of interrupt and memory system for what's been said, as that's beyond the scope of the game right now. But players should be able to move to another room in the middle of a dialogue tree. Conceivably I could create a variable to track whether or not a particular branch is finished, but I think that's for a later date. Right now I want to focus on getting the story/conversation written and in the game.
And no worries, I'm happy to help organize this. I need this as much as everyone else. Not just to be motivated to complete something but to have a conversation with people about things I'm interested in. There's only so much a six-month old can contribute to any conversation.