Okay, I introduced the path ruiner using my mules.
Ignore her, now?
this doesn't work, i tried this so many times.
just befriend the animal that you want to move out.
your BFFs move want to move faster because they feel that they have already done everything they could in your town.
edit: moves are also random. but there's more of a chance that your BFF will ping than someone that you don't talk to as much.
ignore method has always worked for me. also, villagers try to move out more frequently if you have 10. for me, i get a villager asking to move every other day. so if you have 9 i suggest adopting one to get the process moving more quickly. good luck!