You're gonna need to time travel if speed is your concern.
As far as I know, harassing villagers/complaining about them has no effect on who moves out. It's random. I believe the only rule is the newest villager will not ask to move. You also can only move one villager out at a time, because villagers only moves when you have a "full" town. They typically tell you they're moving 7-10 days in the future from when they first ping you. Then you need to wait a few days for a new villager to move in before someone else will ping you to move out. So without time travel it will literally take months to move 6 villagers.
WITH time travel... it's tedious, but if you have the free time you can manage it. I've done it quite a few times to get my house placement organized more quickly, using the following method I found on a guide somewhere:
Wait until your village is full, then TT 2 days into the future, save and quit immediately, then TT back to today. (This is usually enough time for a mover to appear but not always, so you may need to repeat it). Go around trying to get a ping, or talking to every villager at least twice to hear any rumors about someone moving. If they mention hearing a rumor about you (town hero, stump maker, etc) then there is no villager ready to move. Using the megaphone helps find where everyone is to make this go faster.
Once you find out who is moving, get them to ping you about it, tell them to leave, then save and quit. TT to their move out day, go talk to them (in boxes), save and quit, TT back to present day. Then you might need to do the 2 days forward trick a few times until the new villager moves in. Make sure your QR codes are placed all over except where you want the new plot to show up. Once the new villager is there, repeat the whole process.
It'll take a while and it helps to keep a list of who you've spoken to for each "trip". Sometimes villagers you want to stay will ask to move, and if you tell them to stay you then need to wait another few days for the next one to ping you. Also, beautiful town ordinance is recommended since TT forward counts every single day as time passing in the town.
You can do this rapid-fire or you can take advantage of the in-game passage of time to unlock store upgrades, stock up on landscaping items from Leif, breed flowers, expand your home, etc.
