As a lot of people have asked how I'm cycling, I'm just going to put it here.
NOTE: This is how I cycle when I DON'T have dreamies that I really want to keep.
If you have villagers you want to keep, then other methods are far safer.
> The day Isabelle announces "someone new has moved into town", I travel 3 days into the future. Talk to one person until it gets annoyed to see if there's a rumor about someone moving. If not, I move on to the next day, talk to the same person 10 times, and repeat until there's a rumor about someone moving.
> Once there is a rumor, I talk to the person who's moving. Save and quit, then walk in front of the person again, and he/she will ping to move. I tell them to move. Then I TT to the date they're moving. (If they say they'll stay, I just quit the game without saving, and then TT to the date they're moving)
> After someones picked them up, I TT 3 days forward again. Then keep TTing forward 1 day at a time until Isabelle gives the announcement that someone has moved in.
> Start over from the top.