So each time I talk to my villagers it's always Sly or Wart Jr who ask to move. I don't know why it's only ever really them, once it was Muffy but it's generally back and fourth between these boys. I don't want either of them to move so it's super upsetting, I have been trying forever to get Stitches to move but he wont ever ping. I have high friendship with all of my villagers so maybe I should start ignoring the others and JUST talk to Stitches or something? I don't know...
It is odd given wart is cranky, Sly is a jock, and you have two Lazys'.
I'd do a modified version of what you suggest yourself.
Talk to Stitches more, send him a daily letter with a gift and do his tasks - so friendship goes up, and then he might ask to move.
I wouldn't ignore the other villagers though, would talk to all of them as I find the more I interact with them the more they ping me (& hence I find out who is moving).
I do have villagers that have not asked to move (as yet). I guess it is partly random.
Some villagers do become anchored for some bizarre reason. At one point I had 4 villagers who would never ask to leave, it was always the others. And it was mostly Bob for a long time, every 4 days I would get a moving ping and it was usually him.
Just keep at it if you can. I had a problem with Lolly moving out for the last couple of months, tried again a with tt'ing her out last week and finally managed it. She was anchored for a long long time thoigh
I usually talk to all my villagers and pick a random villager to be my "informant" and talk to them until they tell me who wants to move. If Stitches keeps being mean and not moving I'll probably go ahead and let Sly go as I'm not too attached to him, and I could replace him with another jock that is more "Halloween-y", but both him and Stitches have been there since the beginning, in fact I got Stitches as my first "moved in" villager because he auto-voided from my last town when I was transferring stuff over. I don't know if that forces them to stay longer or anything... Stitches was just sick for a few days and I sent him a few letters and gave him medicine each day too and I keep trying to walk by him for pings but he keeps asking me about FOOD! Darn kid wont leave I swear...