Time travel 2 days at a time and talk to everyone. Eventually, the villagers you want to move out will ask you they want to leave. It's really the only way if you want to conserve other villagers and keep them from moving. It's all random and luck based. It's also very tedious haha. I wish you the best of luck!
Whenever I do it, it almost never works and no one pings. I can't even get villagers to talk about it(I'll try for three hours). And then someone randomly leaves in days. I have no idea what I'm doing wrong.