Took me a moment to figure out you were talking about the quest AFTER "Every Little Thing She Does is Magitek", which is called "Escape from Castrum Centri". Presuming this is the case, I found a video with the intermediary cutscene so mentioned. Now, while it isn't -your- character in the cutscene, it'll at least let you read the dialogue that you missed. Sorry I can't be of any more help. And yes, this truly does suck -- just recently I accidentally skipped an intermediate cutscene...too late, too bad, can't view it again.
Here we are:
https://youtu.be/1_zdwTwEXrI?t=8s
EDIT: I should say, I am exactly the same way. I gobble up every little morsel of dialogue. I don't like to skip a thing. People can get impatient with me if I am doing the quests with a group, but I tell them "I'm still reading!". He he. And actually, rereading Glaumunt's explanation, I am reminded of how sad it is. Thank you.
