I'm going to speedrun Nancy Drew: Message in a Haunted Mansion this week! Let's hope there are no major problems.
As far as I can tell, the endgame sequence starts when Nancy spies on Louis. In order to reach that point in the game, Nancy must talk to everyone and get all three tiles. One tile is the attic, which means Nancy has to get the attic key from the saloon, when Charlie isn't there.
Since the game starts at 8:00, and Louis doesn't arrive until noon, you're forced to make three time jumps.
1. Jump to a time when Charlie is absent (so you can steal his key)
2. Jump to a time when Louis is there (so you can talk to him)
3. Jump to a time when Louis isn't there (so you can spy on him)
#2 must happen before #3, but #1 can happen before or after #2. Which gives us two possible routes.
Route 1: (#1 is done first)
Start the game by jumping back an hour, so you can steal Charlie's key. Use it to do the attic stuff. Jump ahead to noon and talk to everyone. Jump back an hour and spy on Louis.
Route 2: (#1 is done second)
Start the game by jumping to noon and talk to everyone. Jump ahead to 5:00 when Charlie leaves. Steal his key and do the attic stuff. Spy on Louis.
It looks like Route 2 is slightly faster! That's because Route 2's second jump leaves Nancy at the 5:00 hour, which is a time when you can spy on Louis. Route 1's second jump puts you at a time where you can't spy on Louis, forcing you to take a third jump. Now, granted, the time difference between the two will be less than a minute, but every little bit helps.