Your answers to the other thread in the development forum made me came to this guess, too. So you might be right. That's why I already thought of a pure crawling mode where you don't need to care about accepting quests first.
My game (that's currently on the backburner) is more story based than the average roguelike, but I'm still keeping multiple playthroughs in mind, because it's still a roguelike. I'm handling this by keeping story sections brief (no fetch quests, missions/quests are short with a high amount of action in them). I'm going to keep the number of NPCs the player needs to talk to low. Any given quest should only require speaking to one person to initiate it, and maybe one other person to finish it, and that's it.
Any story related NPC the player needs to talk to will always have one dialog option to skip everything else they have to say. The only exception is when the player has a decision to make, in which case that option will take them immediately to the decision.
Like say they there's an NPC asking for the player's help against bandits. They might say "We're being attacked by (insert name of bandits)! Help us!"
The player will then be presented with options like this:
> Yes
No
Tell me more about the situation
I assume that the player has played through this before, and saying yes will immediately drop them into the thick of things. If it is their first time, they can choose the third option, which will give more information on what's going on and what they can expect in the mission.
Maybe something like that would work for you?