I never understood the whole 5:59am thing, I always just go to noon (especially when considering checking if a villager is moving out, since you should wait until all villagers are awake before checking and uchis wake up at 11am). Here's what I suggested my boyfriend to try and it worked:
1. If Gracie is there, do the fashion check
2. Make sure no villagers are thinking of moving (make sure it's past 11am) (talk to 3 different villagers all the way through, if someone is moving one of these 3 will tell you).
3. If someone is wanting to move, stop them. If no one is wanting to move, you're good to continue.
4. TT to the next day and load up the game with any of your characters (note: I always TT using the 3DS settings, NOT talking to Isabelle. I feel like it's easier to keep track of and less likely to accidentally erase my town if I'm in a hurry)
5. If no one wanted to move out yesterday and you want to be extra safe, you can check on this day again to see if any villagers are moving out. If you already stopped a villager from leaving yesterday, just continue to step 6.
6. TT back to the previous day, when Gracie was there. She should be there again and you can do another fashion check.
Now if she still hasn't decided to open up shop in your town, you can go back and do the process again.
For peace of mind, you can check each time to see if someone is trying to leave, but you should only need to check every 4 days. Villagers move out 5 days after they initially decide to move, and often wait a couple days to try to move out after the last villager who tried to move. Also keep in mind that if you TT back into the past, it counts as a day into the future (concerning moveouts). So you'd need to take that into consideration if you only check every 4 days. Doing this trick twice would count as 4 days.
If I'm trying to move a villager out, I go forward 3 days, play, and then go forward another day (so in total, 4). By that time a villager is usually trying to move out. I've never accidentally lost a villager.