Ran into the dialogue bug multiple times trying to replicate what causes it. My only idea is that I'm going through it too efficiently, breaking the dialogue sequence. I captured a couple of videos of it happening but not sure how much it'll help.

Hey buddy, thanks for testing out the bug. This screenshot is exactly what I need.
If you haven't run the game since encountering the problem, can I get you to send over the Player text file? That would also help me figure out what's causing it.
To get to the file, you'll need to go type %appdata% in your search bar, click on the folder, then go to LocalLow -> Mackerel Sky -> At Skies Edge. The file should be pretty easy to spot. You can copy the entire log file and put it on https://pastebin.com/ then send me the link to the paste.
Thanks!
I think I have nailed this problem down. Once a a voice line script finishes printing, it is supposed to 'arm' the next script to play after a certain amount of time has passed. This is done through Unity's coroutine functions, and I suspect the problem is that in some circumstances (e.g. if your computer is under load) the coroutines aren't firing properly. I've modified the manager slightly to record the time the next script should be fired. Then it checks whether or not the current in-game time has gone over this flag before arming the next script, so it should run independently of any coroutine nonsense.
I have a video with that bug happening, i needed some restarts to get, maybe restarting the mission makes this happens too?
Here the log too: https://pastebin.com/L4d1VhuM
Here the video: