The way i used is the Cycling. I moved out more than 20 Villagers in less of a month with this process. Complain thing just don't work (at least not for me).
-One thing that can work too is that other Villager move out.
-Not talking with him so he/she going to move out in a week.
Now, an amiibo card will move in onto the same spot, right? So how long would it take to get rid of a village and be able to get them onto a different spot?