Do you have a source on this? I'm very interested in how this mechanic works, I didn't know Ninji had commented on it.I saw this guide: Make sure you DON'T talk to the villager you want to leave. Ninji found that ignoring them helps make them leave. Talk to them only when the thought bubble appears.
Well, this method seems to be the fastest : https://www.belltreeforums.com/threads/how-to-reset-which-villager-is-moving.510949/
You don't have to time travel, I don't, and it still worked. You just have to wait until someone wants to move out and then it should only take a few days for you to be able to say goodbye to the islander you want gone.