Got a fast and (from what I can tell) entirely consistent setup which doesn't require the intro cinematic:
The idea is this: The point of the intro cinematic is to update the save file list (replace the hamlet save file with the dungeon save file). However, other things can trigger that as well, such as exiting to the main menu or starting up the game. Darkest Dungeon doesn't actually save on exit to main menu and it also doesn't save on loading the hamlet, so you can trigger a re-save (e.g. by exiting and entering a room) while you're waiting for the hamlet to load, and then exit to the main menu and immediately enter the dungeon save without needing to refresh the save file list with an intro cinematic.
Note that because you can perform all of the dungeon movement during loading, having more than two Darkest Dungeon instances open at once doesn't matter, since you'll still be throttled by the instance that you're duping on. This note does not necessarily apply to farmstead dupes, if it's determined that those are worth going for.
I wonder if someone with experience with something like cheat engine could figure out if any non-UI related memory addresses actually change with a second load (and if so, what they are).
As a foreword, I'm not really a speedrunner, I just thought I'd share this because it might lead to some kind of skip in the future.
When playing casually, I found that it's possible to make the "load game" dialogue appear twice when loading a save.
Just select your save, and then mash A and UP as fast as possible. If it's fast enough, when you hit the Load button, the dialogue will close and the game will load, but then the "load game" dialogue will appear again. Both load and cancel have the same effect casually (it just loads the game as normal) but it's possible that if you press load on both of the dialogue boxes there could be some double-loading kind of stuff.
Again, I haven't tested any side effects of this, not that I would even know how to. It's possible that pressing load twice does the exact same thing as pressing it once, but depending on the game, small things like this can sometimes be gold mines for strange bugs and glitches.
Here's a video of me executing it (yes, I'm using the Tales of Zestiria Fix mod, but I set my FPS to 30): Things get especially interesting around 1:55
Does this mean that you aren't allowed to run or does it mean you aren't allowed to autorun?