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The secret is taking a nice screenshot of an event (this can take a few tries, but ShareX makes it quicker in "Fixed size region mode") and then immediately adding the entry to the flowchart, before I do anything else.
The layout is fortunately mostly self-arranging: I still have to tell it how the scenes relate to each other and where and how to put the links, but for the most part I don't need to worry about avoiding overlaps.

I've also been using version control software, which makes it easier to see where I left off in the previous session.

A lot of effort went into actually (not)running into the events and branches in the first place, though.
(I wasn't quite testing every possibility, since there's a certain rhythm to the game, which let me guess some of the details.)