Move to a server that isn't overcrowded. I'm on Adamantoise, and there are dozens of plots available in the Goblet, and a handful in each of the other housing areas - there were even a few smalls in Shirogane when I checked last week. The apartment complex in my ward(Goblet 13) also has literally only a single apartment taken up.

FFXIV doesn't have a housing crisis, it has a population crisis specific to certain servers.