Joanna's start-of-game conversation may be a pain to navigate, but the start-of-game conversation with Alejandro del Rio is a snap. He will say the same thing, no matter which conversation options Nancy picks. So, to get through the conversation quickly, just pick the shortest conversation topics.
Taylor's conversation is mostly the same, except occasionally, you have to avoid the conversation options that lead to tangents, like the one about the Board of Directors and the one about the monolith agreement.
Henrik's opening conversation was easy to figure out, because you only have two conversation topics with him. I just recorded all four possible conversations. It turns out that 1-2 is about 0.2 seconds faster than 1-1, so that's the one I'll pick.
That's going to be it for my speedrun, for now. Maybe I'll resume the project sometime in the future, when I'm done with the "Everything Wrong With" series.