if I absolutely was determined to get someone out, this is what I would do:
1. determine if anyone is currently "thinking of leaving". The only sure-fire way to do this, if no-one pings, is to put your 3DS clock a week forward, start your game with a new save file (NOT your mayor, if you do that you can lose someone). You won't save the new character, you only want to get to where you can see the map, and see if anyone is missing. Once you have seen the map, turn the game off without saving, and set your 3DS clock back again to where it originally was.
2. if someone *was* missing from the map, find them and get them to ping to tell you they are thinking about moving. You might have to save and load a few times before you get a ping from them. If it is Lucky, then tell him to move, and you are done! If it is not Lucky, then tell them to stay, and do step 3. If someone wasn't missing from the map, then go right to step 3.
3. Move the game 1 month forward (I use a month because it seems guaranteed to have a new villager "thinking of moving". I used to do 5 days, but then sometimes there wouldn't be a new potential mover). Run around and talk to everyone outside, to get past the "you've been gone so long" discussions. Save, quit, reload, and find the pinger. If you don't get someone pinging to move, then save, quit, reload, and try again. If you still don't find them, then you can use the Step 1 trick to peek and see who it is. If it's not Lucky, then tell them to stay, and repeat step 3 again.
It is a very quick method, and it is what I use in my cycling town when I want to cycle, but I am holding a couple of villagers for others. Despite it being quick, though, the randomness can get you - I cycled through 70 moving pings, then gave up, when trying to get Snake out.