Some advice I've seen on a couple of ACNH Discord servers is to do these step in the following in order:
TT back 15 days
Talk to every villager EXCEPT for the one you want to move (just ignore the one you want to move out)
TT back to the present
The villager you want to move out should be doing the "thinking" animation; talk to them and see if they mention moving. (It's not foolproof though.)
I haven't tried it myself, so I don't know how well it does or doesn't work, but if you have an Amiibo card for a villager and your town is full, you can scan the card to force out the villager you don't want. Hope this helps! ^^