This is exactly what I do. If he's moving, he's waiting to ping you. You need to trigger a ping - saving and quitting will do that. Then you need to get to him before someone else pings you to show you a letter or ask for a new catchphrase. So sneak around them to get to him first. You may need to do it several times to get him outside and to get around everyone else. But if you want him to stay, this is the best way I know
Good luck!
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You have to sneak around that kitty so she doesn't see you!