Okay so, it's obviously best to be on beautiful ordinance for this, but if you TT, I imagine you are anyway, but yeah..
You can just day-by-day until someone pings you and tells you they're moving.. If it's a dreamy, or someone you wanna keep, go through the usual way of stopping them.. Then, you TT 4 days, because it takes 4 days for someone new to try and move out (it can be more than 4, but NEVER less) .. Then, you look around to see who's now pinging you.. However, because you've TT'd so many days in advance, some of your villagers will say (it's been 1 week since we talked) which means they won't ping you, so, you may have someone ping you asking to go to their house, or asking for something.. So, next, you talk to the people you want to keep.. Then you TT day-by-day until someone pings you they're moving, that way, you can stop any dreamies from going.. But you'll also be ignoring any ones you want out, meaning they're more likely to move (however you won't know when they're moving unless another villager tells you)
Sorry for that wall of text, but it is fairly simple
.. It just makes it faster to cycle out villagers