No I meant, the way I wrote should work - but of course, you can't do it if you already have 10 villagers. Have an empty plot, go to an island to invite someone in (or wait for the plot to be sold) and swap the villager before the house is built. This way, it'll work.
We'll call this Sold Plot Theory ? hahah
Anyway, I tried it and IT WORKS! I've successfully gotten Rolf to move into my island.