Sorry for the message influx! I got some answers and it does seem you just need to talk to the villager a few times before they ask to move in sometimes. I'm going idle to work on some stuff so please shoot me a message when you're heading over.
Hey, if you are available to trade now (Pitfall Seed for my Nook Mile Ticket), do you mind dropping it off at my town? No worries if you aren't available or would rather I pick up.