Another system is having an amiibo/getting blessed and using a new villager camp on your island. It's a modest cheaty though. When you eventually convince them (after hours of playing that frickin card game) and they request to kick out someone, keep reloading the game (go into the dash without causing the dialogue and close the game without saving) until they indicate the one you want . If I am not making sense, you will find guides online that explain this better than me
Not sure whether you understand so I hope this suggestion helps, but the basic procedure for moving individuals out is that every fourteen days, a random villager is going to have the cloud bubble above their mind and will ask to proceed. If you see the cloud over somebody that you want to keep's mind, do not speak to them! The bubble will not be on them another day but it won't restart the two week cycle. 1-3 days after another arbitrary villager will be selected to possess the move out bubble. Just keep leaving them thinking (don't talk to them at all that day) until it randomly picks the one you want to move out.
The new remarks they provide you after a very long absence are occasionally pretty thoughtful, as well. I have had some villagers say something to the effect of"have not seen you in x months, I hope you're still happy and taking care of yourself, it's good to see you again" and I'm always like"aw"
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