You readers are fine with me plotting a Nancy Drew speedrun for a week, right? This is kind of a Nancy Drew blog.
Josiah's notebook gives you the carriage door puzzle. The carriage door puzzle has multiple parts.
1. Bard Bounce. Play this in the den.
2. Favorite poet. Look at the book on Emily's bed.
3. Mini-Golf. I hate this puzzle.
4. Gloria's middle name. I'm pretty sure you have to ask Emily for this.
While speed running, I'll have to test all the various combinations, here. Maybe it's like "Legend of Zelda: Ocarina of Time", where the game SAYS you have to get all six medals, but really, the game only checks to see if you got the first and last medals. You can technically skip the others.
So I'll see if any of these four things can be skipped. Hopefully one or more can! I doubt that all four can be skipped. The route will have to adjust, accordingly. Like, if Bard Bounce can be skipped, I won't ever do that. If Gloria's middle name can't be skipped, I have to plan to go back to the Lilac Inn and do that. I have to go back to the Lilac Inn at SOME point, so maybe I can combine two trips?