I've been stuck for around 3 years trying to kick out my 10th villager, but he has yet to move out. If I were to kick out one of my other villagers, would he finally decide to move out?
I have heard that 10th villagers are notoriously difficult, if not downright impossible, to move out. Your best bet would probably be to either kick them out with an Amiibo villager or let another villager move out so you can get a new 10th villager to move in. Once you have a new 10th villager, it will still be random as far as who decides to move, but you'll probably find it a lot easier to get that villager out.